Finite Group Databasebeta

← #25010464

Subgroups — #25010464

Order 11008.

344 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147569C211yesmaximal, characteristic
2#19136819C211yesmaximal, characteristic, complemented
3#19136732C211yesmaximal, characteristic, complemented
4#19133990C211yesmaximal, characteristic, complemented
5#19132640C211yesmaximal, characteristic, complemented
6#19132575C211yesmaximal, characteristic, complemented
7C43×#1331C211yesmaximal, characteristic, complemented
8#14583570—21no—
9#14583304C2211yescharacteristic
10#14583276C2211yescharacteristic
11#14583274—21no—
12#14583110—21no—
13#14583094—21no—
14#14583093—22no—
15C8×Dic86C2211yescharacteristic
16#14582981—21no—
17#14582724—21no—
18C4⋊(C43⋊C16)C2211yescharacteristic
19#14582701—22no—
20#14582700—21no—
21#14582646—21no—
22C4×D8×C43C2211yescharacteristic
23C4×C16×C43C2211yescharacteristic
24C43×#335C2211yescharacteristic
25C2×#10621898—41no—
26C2×Dic172—41no—
27C2×D344—21no—
28C2×D344D412yes—
29C2×#10621882—22no—
30#13063325—21no—
31#13063322—21no—
32#13063321—22no—
33#13063299—41no—
34#13063298—42no—
35C4×Dic86D411yescharacteristic
36#13063287—22no—
37C2×C43⋊C16—21no—
38#13063259—21no—
39#13063259—21no—
40C4⋊(C43⋊C8)D411yescharacteristic
41Dic43⋊C8—21no—
42#13063250—41no—
43#13063245—22no—
44C8×Dic43—21no—
45C2×D8×C43D411yescharacteristic
46C4×D4×C43—21no—
47C2×C16×C43—21no—
48#107×C43D411yescharacteristic
49C4⋊C8×C43—21no—
50#102×C43—21no—
51C4×C8×C43C2311yescharacteristic
52C2×D4×C43—21no—
53C22×C4×C43—41no—
54C2×C22⋊D43—42no—
55C2×C22⋊D43—42no—
56#10621898—82no—
57#10621898—82no—
58C2×D172—22no—
59C2×D172—41no—
60C2×D172—41no—
61C2×C4×D43—42no—
62C2×Dic86—41no—
63C2×Dic86D811yescharacteristic
64D8×C43—21no—
65D8×C43—21no—
66C2×C8×C43—41no—
67C2×C8×C43C2×D411yescharacteristic
68C2×C8×C43C2×D411yescharacteristic
69C4⋊C4×C43—21no—
70C22⋊C4×C43—41no—
71C42×C43C2×D411yescharacteristic
72#10621882—82no—
73(C2×D43)⋊C4—42no—
74C4⋊Dic43—41no—
75C4⋊Dic43—41no—
76C4⋊Dic43D811yescharacteristic
77Dic43⋊C4—21no—
78C4×Dic43—21no—
79C2×C43⋊C8—21no—
80Dic172—82no—
81D344—42no—
82D344—41no—
83D344—41no—
84C16×C43—41no—
85C43⋊C16—41no—
86C23×C43—41no—
87C22×D43—42no—
88D4×C43—41no—
89D4×C43—41no—
90C2×C4×C43—41no—
91C2×C4×C43—81no—
92C2×C4×C43—81no—
93C2×C4×C43#12011yescharacteristic
94C2×C4×C43C2×D811yescharacteristic
95C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
96C22⋊D43—84no—
97C22⋊D43—162no—
98C2×Dic43—21no—
99C2×Dic43—21no—
100C2×Dic43—81no—
101D172—42no—
102D172—42no—
103D172—81no—
104D172—81no—
105D172—161no—
106C4×D43—84no—
107Dic86—21no—
108Dic86—81no—
109Dic86—81no—
110Dic86D1612yes—
111C8×C43—21no—
112C8×C43—81no—
113C8×C43#13511yescharacteristic
114C8×C43#13711yescharacteristic
115C43⋊C8—41no—
116#12380—431nomaximal, Sylow
117C22×C43—81no—
118C22×C43—81no—
119C22×C43—81no—
120C22×C43#44711yescharacteristic
121C2×D43—82no—
122C2×D43—82no—
123C2×D43—82no—
124C4×C43—21no—
125C4×C43—81no—
126C4×C43#45211yescharacteristic
127C4×C43#45511yescharacteristic
128C4×C43C2×D1611yescharacteristic
129C4×C43#50911yescharacteristic
130Dic43—22no—
131Dic43—41no—
132Dic43—161no—
133#3391—431no—
134#2240—431no—
135#2224—431no—
136#1674—431no—
137#1361—431no—
138Q8⋊C16—431no—
139#1331D4311yescharacteristic, complemented
140C2×C43—161no—
141C2×C43#164111yescharacteristic
142C2×C43#218411yescharacteristic
143C2×C43#219411yescharacteristic
144D43—162no—
145#550—861no—
146#500—431no—
147#493—431no—
148#493—861no—
149#462—861no—
150#459—862no—
151#459—861no—
152C8×Q8—431no—
153C4×D8—861no—
154C4×D8C2×D4311yescharacteristic
155#366—861no—
156C4⋊C16—431no—
157#357—862no—
158#357—861no—
159C4×C16C2×D4311yescharacteristic
160#335C2×D4311yescharacteristic
161#332—861no—
162C43#1238011yescharacteristic, complemented, Sylow
163C2×#41—1721no—
164C2×Q16—1721no—
165C2×D8—432no—
166C2×D8—862no—
167C2×D8—861no—
168C2×D8D17211yescharacteristic
169C4⋊Q8—861no—
170#127—862no—
171#127—861no—
172#121—1722no—
173#121—1721no—
174C4×Q8—431no—
175C4×D4—21no—
176C4×D4—862no—
177C2×C16—21no—
178C2×C16—861no—
179#107—861no—
180#107—861no—
181#107D17211yescharacteristic
182C4⋊C8—21no—
183C4⋊C8—431no—
184C4⋊C8—861no—
185#103—1721no—
186#102—21no—
187#102—862no—
188C4×C8—861no—
189C4×C8C22×D4311yescharacteristic
190#41—3442no—
191#41—3442no—
192C2×Q8—431no—
193C2×Q8—1721no—
194C2×D4—21no—
195C2×D4—862no—
196C2×D4—1722no—
197C2×D4—1722no—
198C2×D4—1721no—
199C2×D4—1721no—
200C22×C4—41no—
201C22×C4—1722no—
202Q16—3442no—
203D8—21no—
204D8—21no—
205D8—3442no—
206D8—1722no—
207D8—1721no—
208D8—1721no—
209C2×C8—41no—
210C2×C8—861no—
211C2×C8C2×D17211yescharacteristic
212C2×C8D4×D4311yescharacteristic
213C4⋊C4—21no—
214C4⋊C4—431no—
215C4⋊C4—861no—
216C4⋊C4—1721no—
217C4⋊C4—1721no—
218C22⋊C4—41no—
219C22⋊C4—1722no—
220C42—861no—
221C42D4×D4311yescharacteristic
222C16—41no—
223C16—1721no—
224C23—41no—
225C23—1722no—
226Q8—432no—
227Q8—861no—
228Q8—3441no—
229Q8—3441no—
230D4—41no—
231D4—41no—
232D4—3444no—
233D4—3441no—
234D4—3441no—
235D4—1722no—
236D4—1722no—
237D4—6881no—
238D4—6882no—
239C2×C4—41no—
240C2×C4—81no—
241C2×C4—81no—
242C2×C4—861no—
243C2×C4—861no—
244C2×C4—3444no—
245C2×C4—3441no—
246C2×C4#1306329511yescharacteristic
247C2×C4D8×D4311yescharacteristic
248C2×C4#1306335211yescharacteristic
249C8—21no—
250C8—81no—
251C8—1721no—
252C8#1306334711yescharacteristic
253C8#1306335811yescharacteristic
254C22—81no—
255C22—81no—
256C22—81no—
257C22—3442no—
258C22—3442no—
259C22—3442no—
260C22#1458303411yescharacteristic
261C4—21no—
262C4—81no—
263C4—862no—
264C4—1721no—
265C4—6881no—
266C4#1458306311yescharacteristic
267C4#1458307811yescharacteristic
268C4D16×D4311yescharacteristic
269C4#1458333611yescharacteristic
270C2—161no—
271C2—6882no—
272C2#1913379111yescharacteristic
273C2#1913650811yescharacteristic
274C2#1913656711yescharacteristic
subgroupG/H
centerC22#14583034
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#1331C2
socleC22×C43#447
prime radical#19147569C2
hypercenter#1331D43
hypocenterC43#12380
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1331

Complements

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

NH ≅ G/Ntype
2. #19136819C2semidirect
3. #19136732C2semidirect
4. #19133990C2semidirect
5. #19132640C2semidirect
6. #19132575C2semidirect
7. C43×#1331C2semidirect
139. #1331D43semidirect
162. C43#12380semidirect

Maximal subgroups

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

subgroupindex
#191475692
#191368192
#191367322
#191339902
#191326402
#191325752
C43×#13312
#1238043