Finite Group Databasebeta

← #24993477

Subgroups — #24993477

Order 11008.

474 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144411C211yesmaximal, characteristic
2#19143713C211yesmaximal, characteristic
3#19135517C211yesmaximal, characteristic, complemented
4#19134612C211yesmaximal, characteristic
5#19133281C211yesmaximal, characteristic, complemented
6#19132496C211yesmaximal, characteristic, complemented
7C43×#1292C211yesmaximal, characteristic, complemented
8C2×#13063325C2211yescharacteristic
9C4×#10621898C2211yescharacteristic
10#14583195C412yescomplemented
11#14583190C412yescomplemented
12#14583185—21no—
13#14583180—21no—
14#14583026—21no—
15#14582976—21no—
16#14582970—22no—
17#14582955—21no—
18#14582952C2211yescharacteristic
19#14582941—21no—
20#14582921—21no—
21C2×#13063251—21no—
22#14582901—21no—
23C2×#13063250—22no—
24C4×C4⋊Dic43C2211yescharacteristic
25#14582660—21no—
26#14582644—21no—
27#14582644—21no—
28C43×#423C2211yescharacteristic
29C43×#423C2211yescharacteristic
30C2×C4⋊C8×C43C2211yescharacteristic
31C2×#10621898D411yescharacteristic
32C22×Dic86—21no—
33C2×#10621872—22no—
34#13063325—21no—
35#13063325—21no—
36#13063325—21no—
37#13063325C2×C412yes—
38C4×Dic86C2×C411yescharacteristic
39C4×Dic86D411yescharacteristic
40C4×D172C2×C411yescharacteristic
41C4×D172D411yescharacteristic
42C4×C22⋊D43—21no—
43C4×C22⋊D43—21no—
44#13063284D411yescharacteristic
45#13063282—21no—
46C2×C4⋊Dic43—21no—
47C2×C4⋊Dic43—21no—
48C2×C4⋊Dic43—21no—
49C2×C4×Dic43—21no—
50C42×D43—21no—
51#13063259—22no—
52#13063257—22no—
53C4⋊(C43⋊C8)D411yescharacteristic
54C4⋊(C43⋊C8)D411yescharacteristic
55Dic43⋊C8—22no—
56#13063251—42no—
57#13063250—22no—
58#13063250—44no—
59#13063247—22no—
60C22⋊(C43⋊C8)—21no—
61(C2×D43)⋊C8—22no—
62#13063235—22no—
63C4×C43⋊C8—21no—
64C43⋊#95—21no—
65C2×M16×C43—21no—
66C2×M16×C43—21no—
67C22×C8×C43D412yes—
68C2×C42×C43C2311yescharacteristic
69C4⋊C8×C43—21no—
70C4⋊C8×C43—21no—
71C4⋊C8×C43—21no—
72C4⋊C8×C43—21no—
73C4⋊C8×C43—21no—
74C4⋊C8×C43C2×C412yes—
75C22×C4×C43C2×D411yescharacteristic
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43#4111yescharacteristic
78C2×C22⋊D43—21no—
79C22×Dic43—41no—
80C22×Dic43—41no—
81#10621898—21no—
82#10621898—21no—
83#10621898—21no—
84#10621898—21no—
85C2×D172C22⋊C411yescharacteristic
86C2×C4×D43—21no—
87C2×C4×D43—21no—
88C2×C4×D43—21no—
89C2×Dic86—22no—
90C2×Dic86—42no—
91C2×Dic86—42no—
92C2×Dic86—41no—
93C2×Dic86C22⋊C411yescharacteristic
94M16×C43—41no—
95M16×C43—41no—
96M16×C43—41no—
97M16×C43—41no—
98C2×C8×C43—22no—
99C2×C8×C43—22no—
100C2×C8×C43—42no—
101C2×C8×C43—41no—
102C42×C43C22×C411yescharacteristic
103C42×C43C2×D411yescharacteristic
104C42×C43C2×D411yescharacteristic
105C42×C43#4111yescharacteristic
106C22⋊Dic43—21no—
107(C2×D43)⋊C4—21no—
108(C2×D43)⋊C4—21no—
109C4⋊Dic43—22no—
110C4⋊Dic43—22no—
111C4⋊Dic43—22no—
112C4⋊Dic43—41no—
113C4⋊Dic43—41no—
114C4⋊Dic43—41no—
115C4⋊Dic43C22⋊C411yescharacteristic
116C4⋊Dic43C22⋊C411yescharacteristic
117Dic43⋊C4—21no—
118Dic43⋊C4—21no—
119C4×Dic43—21no—
120C4×Dic43—21no—
121C4×Dic43—21no—
122C4×Dic43—41no—
123C4×Dic43—41no—
124C2×C43⋊C8—21no—
125C2×C43⋊C8—21no—
126#10621872—82no—
127C23×C43#12111yescharacteristic
128C22×D43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—41no—
132C2×C4×C43C2×C22⋊C411yescharacteristic
133C2×C4×C43C4×D411yescharacteristic
134C2×C4×C43C4×D411yescharacteristic
135C2×C4×C43#12011yescharacteristic
136C2×C4×C43#12111yescharacteristic
137C2×C4×C43#12311yescharacteristic
138C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C43#13711yescharacteristic
140C2×C4×C43#13711yescharacteristic
141C2×C4×C43#13711yescharacteristic
142C22⋊D43—41no—
143C22⋊D43—41no—
144C2×Dic43—21no—
145C2×Dic43—21no—
146C2×Dic43—21no—
147C2×Dic43—42no—
148C2×Dic43—42no—
149C2×Dic43—82no—
150C2×Dic43—81no—
151C2×Dic43—81no—
152D172—21no—
153D172—21no—
154C4×D43—41no—
155C4×D43—41no—
156C4×D43—41no—
157C4×D43—41no—
158C4×D43—81no—
159Dic86—21no—
160Dic86—21no—
161Dic86—44no—
162Dic86—81no—
163Dic86—81no—
164C8×C43—42no—
165C8×C43—42no—
166C8×C43—81no—
167C43⋊C8—41no—
168C43⋊C8—41no—
169#9321—431nomaximal, Sylow
170C22×C43—21no—
171C22×C43—21no—
172C22×C43#38611yescharacteristic
173C22×C43#46811yescharacteristic
174C22×C43#47011yescharacteristic
175C2×D43—41no—
176C2×D43—41no—
177C2×D43—41no—
178C4×C43—21no—
179C4×C43—21no—
180C4×C43—21no—
181C4×C43#41711yescharacteristic
182C4×C43#41911yescharacteristic
183C4×C43#45311yescharacteristic
184C4×C43#45411yescharacteristic
185C4×C43#46811yescharacteristic
186C4×C43#47011yescharacteristic
187Dic43—41no—
188Dic43—41no—
189Dic43—41no—
190Dic43—82no—
191Dic43—82no—
192#3079—431no—
193#2989—431no—
194#1981—431no—
195#1806—431no—
196#1549—431no—
197#1303—431no—
198#1292D4311yescharacteristic, complemented
199C2×C43—21no—
200C2×C43—21no—
201C2×C43#188311yescharacteristic
202C2×C43#189411yescharacteristic
203C2×C43#190211yescharacteristic
204D43—81no—
205C2×C4⋊Q8—431no—
206C4×#41—431no—
207#477—432no—
208#476—432no—
209#475—861no—
210#474—861no—
211#446—861no—
212#436—861no—
213#435—862no—
214#432—861no—
215#431—431no—
216#428—861no—
217#423—861no—
218#423C2×D4311yescharacteristic
219#423C2×D4311yescharacteristic
220C2×C4⋊C8C2×D4311yescharacteristic
221C2×#104—861no—
222#417—861no—
223C2×#103—862no—
224C4×C4⋊C4—431no—
225#339—861no—
226#332—861no—
227#332—861no—
228C43#932111yescharacteristic, complemented, Sylow
229C2×#41—431no—
230C22×Q8—861no—
231C2×M16—21no—
232C2×M16—21no—
233C2×M16—862no—
234C22×C8D17212yes—
235C4⋊Q8—432no—
236C4⋊Q8—861no—
237C4⋊Q8—861no—
238C4⋊Q8—861no—
239C4×Q8—431no—
240C4×Q8—431no—
241C4×D4—431no—
242C4×D4—431no—
243C4×D4—861no—
244C4×D4—861no—
245#117—431no—
246#117—861no—
247C2×C4⋊C4—861no—
248C2×C4⋊C4—861no—
249C2×C4⋊C4—861no—
250C2×C42—861no—
251C2×C42—861no—
252C2×C42C22×D4311yescharacteristic
253#107—862no—
254#106—862no—
255C4⋊C8—21no—
256C4⋊C8—21no—
257C4⋊C8—21no—
258C4⋊C8—21no—
259C4⋊C8—21no—
260C4⋊C8—431no—
261C4⋊C8—431no—
262C4⋊C8—862no—
263C4⋊C8C4×D4312yes—
264#104—1722no—
265#103—862no—
266#103—1724no—
267#102—862no—
268C22⋊C8—862no—
269C22⋊C8—861no—
270#97—862no—
271C4×C8—861no—
272#95—861no—
273#41—861no—
274#41—861no—
275#41—861no—
276#41—861no—
277C2×Q8—431no—
278C2×Q8—862no—
279C2×Q8—1722no—
280C2×Q8—1722no—
281C2×Q8—1721no—
282C2×D4—431no—
283C2×D4—861no—
284C22×C4—861no—
285C22×C4—861no—
286C22×C4—861no—
287C22×C4—1721no—
288C22×C4—1721no—
289C22×C4C2×D17211yescharacteristic
290C22×C4D4×D4311yescharacteristic
291C22×C4#1062190211yescharacteristic
292M16—41no—
293M16—41no—
294M16—41no—
295M16—41no—
296M16—3442no—
297C2×C8—22no—
298C2×C8—22no—
299C2×C8—42no—
300C2×C8—41no—
301C2×C8—861no—
302C2×C8—861no—
303C4⋊C4—431no—
304C4⋊C4—431no—
305C4⋊C4—862no—
306C4⋊C4—861no—
307C4⋊C4—861no—
308C4⋊C4—862no—
309C4⋊C4—862no—
310C4⋊C4—1721no—
311C4⋊C4—1721no—
312C4⋊C4—1721no—
313C22⋊C4—861no—
314C22⋊C4—861no—
315C22⋊C4—861no—
316C42—861no—
317C42—861no—
318C42—861no—
319C42—1721no—
320C42—1721no—
321C42C2×C4×D4311yescharacteristic
322C42#1062189811yescharacteristic
323C42D4×D4311yescharacteristic
324C42D4×D4311yescharacteristic
325C23—861no—
326C23#1306330011yescharacteristic
327Q8—861no—
328Q8—861no—
329Q8—3441no—
330Q8—3441no—
331Q8—1724no—
332D4—861no—
333D4—861no—
334D4—1721no—
335D4—1721no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—41no—
339C2×C4—861no—
340C2×C4—861no—
341C2×C4—861no—
342C2×C4—3441no—
343C2×C4—3442no—
344C2×C4—3441no—
345C2×C4—3441no—
346C2×C4—1722no—
347C2×C4—1722no—
348C2×C4—1721no—
349C2×C4—1721no—
350C2×C4—1721no—
351C2×C4—1721no—
352C2×C4C22⋊C4×D4311yescharacteristic
353C2×C4#1306328711yescharacteristic
354C2×C4C4×D17211yescharacteristic
355C2×C4#1306329511yescharacteristic
356C2×C4#1306329811yescharacteristic
357C2×C4#1306331011yescharacteristic
358C2×C4#1306334911yescharacteristic
359C2×C4#1306335411yescharacteristic
360C2×C4#1306335411yescharacteristic
361C2×C4#1306335711yescharacteristic
362C8—42no—
363C8—42no—
364C8—81no—
365C8—1721no—
366C8—1721no—
367C22—21no—
368C22—21no—
369C22—1721no—
370C22—1721no—
371C22—1721no—
372C22#1458277711yescharacteristic
373C22#1458314611yescharacteristic
374C22#1458315811yescharacteristic
375C4—21no—
376C4—21no—
377C4—21no—
378C4—3442no—
379C4—3442no—
380C4—1721no—
381C4—1721no—
382C4—1721no—
383C4#1458289711yescharacteristic
384C4#1458290611yescharacteristic
385C4#1458306911yescharacteristic
386C4#1458307411yescharacteristic
387C4#1458314411yescharacteristic
388C4#1458315611yescharacteristic
389C2—21no—
390C2—21no—
391C2—3441no—
392C2#1913497011yescharacteristic
393C2#1913502711yescharacteristic
394C2#1913506911yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1292C2
socleC22×C43#386
prime radicalC2×#10621898D4
cosocleC2×C42×C43C23
hypercenter#1292D43
hypocenterC43#9321
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1292

Complements

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

NH ≅ G/Ntype
3. #19135517C2semidirect
5. #19133281C2semidirect
6. #19132496C2semidirect
7. C43×#1292C2semidirect
10. #14583195C4semidirect
11. #14583190C4semidirect
198. #1292D43semidirect
228. C43#9321semidirect

Maximal subgroups

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

subgroupindex
#191444112
#191437132
#191355172
#191346122
#191332812
#191324962
C43×#12922
#932143