Finite Group Databasebeta

← #24993240

Subgroups — #24993240

Order 11008.

478 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145720C211yesmaximal, characteristic
2#19135568C211yesmaximal, characteristic, complemented
3#19133277C211yesmaximal, characteristic, complemented
4#19133155C211yesmaximal, characteristic
5#19132455C211yesmaximal, characteristic, complemented
6#19132426C211yesmaximal, characteristic, complemented
7C43×#2932C211yesmaximal, characteristic
8C2×#13063325C2211yescharacteristic
9#14583295C412yescomplemented
10#14583245C412yescomplemented
11#14583215—22no—
12#14583189—22no—
13#14582952C2211yescharacteristic
14#14582952C2211yescharacteristic
15#14582765C2211yescharacteristic
16#14582662—21no—
17#14582662—21no—
18#14582647—22no—
19#14582633—22no—
20C2×#131×C43—21no—
21C43×#532C2211yescharacteristic
22C43×#435—22no—
23C43×#435—22no—
24C43×#423C2211yescharacteristic
25C43×#408—21no—
26C2×#97×C43C2211yescharacteristic
27C22×Dic86—21no—
28#13063325—21no—
29#13063325—21no—
30#13063325—21no—
31#13063325C2×C412yes—
32C2×C4⋊Dic43—21no—
33C2×C4⋊Dic43—21no—
34C2×C4⋊Dic43—21no—
35#13063256—24no—
36C4⋊(C43⋊C8)—21no—
37C4⋊(C43⋊C8)—21no—
38#13063246—24no—
39C22⋊(C43⋊C8)—21no—
40C22⋊(C43⋊C8)—21no—
41C4×C43⋊C8—21no—
42C4×C43⋊C8C2×C412yes—
43C43⋊#95—21no—
44C43⋊#95—21no—
45C2×#41×C43—21no—
46#131×C43—42no—
47#131×C43—42no—
48C2×M16×C43—22no—
49C2×M16×C43—21no—
50C22×C8×C43—22no—
51C22×C8×C43D411yescharacteristic
52C22×C8×C43D411yescharacteristic
53C4⋊Q8×C43C2×C411yescharacteristic
54#127×C43C2×C411yescharacteristic
55#124×C43—21no—
56#121×C43—21no—
57#121×C43D412yes—
58C4×D4×C43—21no—
59C4×D4×C43D412yes—
60C2×C42×C43C2311yescharacteristic
61C4⋊C8×C43—21no—
62C4⋊C8×C43D412yes—
63C22⋊C8×C43—24no—
64#97×C43—21no—
65#97×C43—21no—
66#41×C43—41no—
67#41×C43—41no—
68#41×C43—41no—
69#41×C43—41no—
70C2×Q8×C43—21no—
71C2×D4×C43—21no—
72C2×D4×C43—21no—
73C2×D4×C43—22no—
74C2×D4×C43C22⋊C412yes—
75C22×C4×C43—22no—
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43C2×D411yescharacteristic
78C22×C4×C43#4111yescharacteristic
79C22×Dic43—41no—
80C22×Dic43—41no—
81C2×Dic86—22no—
82C2×Dic86—41no—
83C2×Dic86—82no—
84M16×C43—44no—
85M16×C43—41no—
86M16×C43—41no—
87C2×C8×C43—21no—
88C2×C8×C43—21no—
89C2×C8×C43—21no—
90C2×C8×C43—22no—
91C2×C8×C43—21no—
92C2×C8×C43—21no—
93C2×C8×C43—44no—
94C2×C8×C43SD1612yes—
95C4⋊C4×C43—21no—
96C4⋊C4×C43C22⋊C412yes—
97C22⋊C4×C43—22no—
98C22⋊C4×C43—22no—
99C42×C43C22×C411yescharacteristic
100C42×C43C2×D411yescharacteristic
101C42×C43C2×D411yescharacteristic
102C42×C43#4111yescharacteristic
103C4⋊Dic43—22no—
104C4⋊Dic43—22no—
105C4⋊Dic43—41no—
106C4⋊Dic43—41no—
107C4⋊Dic43—41no—
108C4⋊Dic43—41no—
109C2×C43⋊C8—22no—
110C2×C43⋊C8—41no—
111C23×C43—22no—
112C23×C43#12111yescharacteristic
113Q8×C43—41no—
114Q8×C43—41no—
115D4×C43—42no—
116D4×C43—42no—
117D4×C43—42no—
118D4×C43—41no—
119D4×C43—41no—
120D4×C43—81no—
121C2×C4×C43—22no—
122C2×C4×C43—41no—
123C2×C4×C43—41no—
124C2×C4×C43—42no—
125C2×C4×C43—42no—
126C2×C4×C43C2×C22⋊C411yescharacteristic
127C2×C4×C43C4×D411yescharacteristic
128C2×C4×C43C4×D411yescharacteristic
129C2×C4×C43#12011yescharacteristic
130C2×C4×C43#12111yescharacteristic
131C2×C4×C43#12311yescharacteristic
132C2×C4×C43C2×SD1611yescharacteristic
133C2×C4×C43#13511yescharacteristic
134C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C43#13711yescharacteristic
136C2×Dic43—42no—
137C2×Dic43—82no—
138C2×Dic43—81no—
139C2×Dic43—81no—
140C2×Dic43—81no—
141Dic86—82no—
142Dic86—82no—
143C8×C43—22no—
144C8×C43—42no—
145C8×C43—41no—
146C43⋊C8—42no—
147C43⋊C8—81no—
148#9287—431nomaximal, Sylow
149C22×C43—21no—
150C22×C43—21no—
151C22×C43—42no—
152C22×C43—42no—
153C22×C43—42no—
154C22×C43#38611yescharacteristic
155C22×C43#46111yescharacteristic
156C22×C43#46311yescharacteristic
157C4×C43—21no—
158C4×C43—21no—
159C4×C43—21no—
160C4×C43—21no—
161C4×C43—42no—
162C4×C43C4×SD1611yescharacteristic
163C4×C43#44011yescharacteristic
164C4×C43#45011yescharacteristic
165C4×C43#45211yescharacteristic
166Dic43—82no—
167Dic43—161no—
168#3227—431no—
169#2932D4311yescharacteristic
170#1993—431no—
171#1548—431no—
172#1517—431no—
173#1286—431no—
174#1275—431no—
175C2×C43—21no—
176C2×C43—21no—
177C2×C43—82no—
178C2×C43#187711yescharacteristic
179C2×C43#190311yescharacteristic
180C2×C43#190911yescharacteristic
181C2×#131—21no—
182#532C2×D4311yescharacteristic
183C2×C4⋊Q8—431no—
184#498—432no—
185#486—432no—
186#481—862no—
187#476—862no—
188#435—22no—
189#435—22no—
190#431—431no—
191#431—431no—
192#423C2×D4311yescharacteristic
193#408—21no—
194C2×#97C2×D4311yescharacteristic
195#382—431no—
196#340—861no—
197#340—861no—
198#333—862no—
199#327—862no—
200C43#928711yescharacteristic, complemented, Sylow
201C2×#41—21no—
202C22×Q8—861no—
203#131—42no—
204#131—42no—
205C2×M16—22no—
206C2×M16—21no—
207C22×C8—22no—
208C22×C8C22⋊D4311yescharacteristic
209C22×C8C22⋊D4311yescharacteristic
210C4⋊Q8—432no—
211C4⋊Q8—861no—
212C4⋊Q8—861no—
213C4⋊Q8—861no—
214C4⋊Q8C4×D4311yescharacteristic
215#127C4×D4311yescharacteristic
216#124—21no—
217#121—21no—
218#121D17212yes—
219C4×D4—21no—
220C4×D4C22⋊D4312yes—
221C2×C4⋊C4—861no—
222C2×C4⋊C4—861no—
223C2×C4⋊C4—861no—
224C2×C42C22×D4311yescharacteristic
225#106—864no—
226C4⋊C8—21no—
227C4⋊C8—861no—
228C4⋊C8—861no—
229C4⋊C8C22⋊D4312yes—
230#102—864no—
231C22⋊C8—24no—
232C22⋊C8—861no—
233C22⋊C8—861no—
234#97—21no—
235#97—21no—
236C4×C8—432no—
237C4×C8—861no—
238#95—861no—
239#95—861no—
240#41—41no—
241#41—41no—
242#41—41no—
243#41—41no—
244C2×Q8—21no—
245C2×Q8—862no—
246C2×Q8—3442no—
247C2×Q8—1721no—
248C2×D4—22no—
249C2×D4—21no—
250C2×D4—21no—
251C2×D4(C2×D43)⋊C412yes—
252C22×C4—22no—
253C22×C4—1721no—
254C22×C4—1721no—
255C22×C4C2×D17211yescharacteristic
256C22×C4#1062189811yescharacteristic
257C22×C4C2×C22⋊D4311yescharacteristic
258M16—44no—
259M16—41no—
260M16—41no—
261C2×C8—21no—
262C2×C8—21no—
263C2×C8—21no—
264C2×C8—22no—
265C2×C8—21no—
266C2×C8—21no—
267C2×C8—44no—
268C2×C8—862no—
269C2×C8—1721no—
270C2×C8#1062188312yes—
271C4⋊C4—21no—
272C4⋊C4—862no—
273C4⋊C4—862no—
274C4⋊C4—1721no—
275C4⋊C4—1721no—
276C4⋊C4—1721no—
277C4⋊C4—1721no—
278C4⋊C4(C2×D43)⋊C412yes—
279C22⋊C4—22no—
280C22⋊C4—22no—
281C42C2×C4×D4311yescharacteristic
282C42#1062189811yescharacteristic
283C42C2×C22⋊D4311yescharacteristic
284C42C2×C22⋊D4311yescharacteristic
285C23—22no—
286C23#1306329911yescharacteristic
287Q8—41no—
288Q8—41no—
289Q8—3442no—
290Q8—3442no—
291D4—42no—
292D4—42no—
293D4—42no—
294D4—41no—
295D4—41no—
296D4—81no—
297C2×C4—22no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—3442no—
303C2×C4—3441no—
304C2×C4—3441no—
305C2×C4—3441no—
306C2×C4—1722no—
307C2×C4C2×(C2×D43)⋊C411yescharacteristic
308C2×C4C4×C22⋊D4311yescharacteristic
309C2×C4C4×C22⋊D4311yescharacteristic
310C2×C4#1306329411yescharacteristic
311C2×C4#1306329911yescharacteristic
312C2×C4#1306330811yescharacteristic
313C2×C4C2×#1062188311yescharacteristic
314C2×C4#1306334511yescharacteristic
315C2×C4#1306335111yescharacteristic
316C2×C4#1306335511yescharacteristic
317C8—22no—
318C8—42no—
319C8—41no—
320C8—3441no—
321C8—1722no—
322C22—21no—
323C22—21no—
324C22—42no—
325C22—42no—
326C22—42no—
327C22#1458277811yescharacteristic
328C22#1458310411yescharacteristic
329C22#1458311411yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—42no—
335C4—3442no—
336C4—6881no—
337C4C4×#1062188311yescharacteristic
338C4#1458299911yescharacteristic
339C4#1458305011yescharacteristic
340C4#1458306111yescharacteristic
341C2—21no—
342C2—21no—
343C2—82no—
344C2#1913492911yescharacteristic
345C2#1913507511yescharacteristic
346C2#1913511711yescharacteristic
subgroupG/H
centerC22#14582778
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2932C2
socleC22×C43#386
prime radicalC43×#532C22
cosocleC2×C42×C43C23
hypercenter#2932D43
hypocenterC43#9287
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2932

Complements

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

NH ≅ G/Ntype
2. #19135568C2semidirect
3. #19133277C2semidirect
5. #19132455C2semidirect
6. #19132426C2semidirect
9. #14583295C4semidirect
10. #14583245C4semidirect
200. C43#9287semidirect

Maximal subgroups

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

subgroupindex
#191457202
#191355682
#191332772
#191331552
#191324552
#191324262
C43×#29322
#928743