Finite Group Databasebeta

← #25010848

Subgroups — #25010848

Order 11008.

224 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 59 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#19136851C211yesmaximal, characteristic, complemented
2#19136677C211yesmaximal, characteristic, complemented
3#19136672C211yesmaximal, characteristic
4#19136433C211yesmaximal, characteristic, complemented
5#19132633C211yesmaximal, characteristic, complemented
6#19132631C211yesmaximal, characteristic, complemented
7C43×#1373C211yesmaximal, characteristic, complemented
8#14583342—21no—
9#14583337—21no—
10C2×#13063270—21no—
11C2×#13063270—21no—
12#14583315—21no—
13#14583279C2211yescharacteristic
14#14583276C2211yescharacteristic
15#14583017C2211yescharacteristic
16#14582720C2211yescharacteristic
17#14582716—21no—
18#14582713—21no—
19#14582682—21no—
20C43×#364C2211yescharacteristic
21C43×#364C2211yescharacteristic
22C4×C16×C43C2211yescharacteristic
23#13063347D411yescharacteristic
24C2×Dic172—21no—
25C2×Dic172—21no—
26C2×D344—21no—
27C2×D344—21no—
28#13063331—21no—
29#13063325—21no—
30#13063322—21no—
31Dic344—41no—
32#13063270—42no—
33#13063270—41no—
34#13063270—41no—
35#13063270—41no—
36#13063270—41no—
37D688—41no—
38#13063265—21no—
39#13063264—41no—
40C16×D43—41no—
41#13063261D411yescharacteristic
42#13063253—21no—
43M32×C43—21no—
44M32×C43—21no—
45C2×C16×C43D411yescharacteristic
46C2×C16×C43D411yescharacteristic
47C4×C8×C43C2311yescharacteristic
48#10621898—21no—
49C2×D172—41no—
50C2×D172—81no—
51C2×Dic86—41no—
52C2×C8×C43C2×D411yescharacteristic
53C2×C8×C43C2×D411yescharacteristic
54C42×C43#4111yescharacteristic
55C4⋊Dic43—81no—
56#10621877—21no—
57Dic172—41no—
58Dic172—41no—
59Dic172—41no—
60Dic172—41no—
61Dic172D811yescharacteristic
62D344—41no—
63D344—41no—
64D344—41no—
65D344—41no—
66D344D811yescharacteristic
67#10621873—21no—
68#10621872—41no—
69C8×D43—41no—
70C16×C43—21no—
71C16×C43—41no—
72C16×C43—41no—
73C16×C43D811yescharacteristic
74C16×C43D811yescharacteristic
75C43⋊C16—41no—
76C22×D43—81no—
77C2×C4×C43—21no—
78C2×C4×C43#12111yescharacteristic
79C22⋊D43—41no—
80C2×Dic43—81no—
81D172—21no—
82D172—81no—
83D172—81no—
84D172—162no—
85C4×D43—41no—
86Dic86—21no—
87Dic86—81no—
88Dic86—81no—
89C8×C43C2×D811yescharacteristic
90C8×C43C2×D811yescharacteristic
91C8×C43#13511yescharacteristic
92C8×C43AGL(1,ℤ/8)11yescharacteristic
93C43⋊C8—41no—
94#12438—431nomaximal, Sylow
95C22×C43#47211yescharacteristic
96C2×D43—41no—
97C2×D43—162no—
98C2×D43—161no—
99C4×C43—22no—
100C4×C43#45911yescharacteristic
101C4×C43#46611yescharacteristic
102Dic43—41no—
103Dic43—161no—
104#2248—431no—
105#2214—431no—
106#2213—431no—
107#2170—431no—
108#1373D4311yescharacteristic, complemented
109#1358—431no—
110#1357—431no—
111C2×C43—21no—
112C2×C43#166711yescharacteristic
113D43—81no—
114D43—321no—
115#510—861no—
116#509—861no—
117C2×SD32—861no—
118C2×SD32—861no—
119#504—861no—
120#494—431no—
121#493—431no—
122#443—431no—
123#364—431no—
124#364C2×D4311yescharacteristic
125#364C2×D4311yescharacteristic
126#362—861no—
127#361—861no—
128#350—861no—
129C4×C16C2×D4311yescharacteristic
130C43#1243811yescharacteristic, complemented, Sylow
131#135—431no—
132C2×Q16—861no—
133C2×Q16—861no—
134C2×D8—861no—
135C2×D8—861no—
136#131—861no—
137C4⋊Q8—861no—
138#127—861no—
139Q32—1721no—
140SD32—1722no—
141SD32—1721no—
142SD32—1721no—
143SD32—1721no—
144SD32—1721no—
145D16—1721no—
146M32—21no—
147M32—21no—
148M32—861no—
149M32—1721no—
150C2×C16—1721no—
151C2×C16D17211yescharacteristic
152C2×C16D17211yescharacteristic
153#108—431no—
154#104—861no—
155C4×C8C22×D4311yescharacteristic
156#41—861no—
157C2×Q8—1721no—
158C2×D4—3441no—
159C2×D4—1721no—
160Q16—431no—
161Q16—1721no—
162Q16—1721no—
163Q16—1721no—
164Q16—1721no—
165SD16—861no—
166D8—431no—
167D8—1721no—
168D8—1721no—
169D8—1721no—
170D8—1721no—
171M16—861no—
172M16—1721no—
173C2×C8—1721no—
174C2×C8C2×D17211yescharacteristic
175C2×C8D4×D4311yescharacteristic
176C4⋊C4—3441no—
177C42#1062190211yescharacteristic
178C16—21no—
179C16—41no—
180C16—41no—
181C16—1721no—
182C16D34411yescharacteristic
183C16D34411yescharacteristic
184C23—3441no—
185Q8—861no—
186Q8—3441no—
187Q8—3441no—
188D4—861no—
189D4—3441no—
190D4—3441no—
191D4—1721no—
192D4—6882no—
193C2×C4—21no—
194C2×C4—3441no—
195C2×C4—1721no—
196C2×C4#1306330011yescharacteristic
197C8—1721no—
198C8D8×D4311yescharacteristic
199C8C2×D34411yescharacteristic
200C8#1306334811yescharacteristic
201C8#1306335311yescharacteristic
202C22—1721no—
203C22—6882no—
204C22—6881no—
205C22#1458317011yescharacteristic
206C4—22no—
207C4—1721no—
208C4—6881no—
209C4#1458309511yescharacteristic
210C4#1458313611yescharacteristic
211C2—21no—
212C2—3441no—
213C2—13761no—
214C2#1913395111yescharacteristic
subgroupG/H
centerC2#19133951
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#1373C2
socleC2×C43#1667
prime radical#19136672C2
hypercenter#1373D43
hypocenterC43#12438
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #1373

Complements

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

NH ≅ G/Ntype
1. #19136851C2semidirect
2. #19136677C2semidirect
4. #19136433C2semidirect
5. #19132633C2semidirect
6. #19132631C2semidirect
7. C43×#1373C2semidirect
108. #1373D43semidirect
130. C43#12438semidirect

Maximal subgroups

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

subgroupindex
#191368512
#191366772
#191366722
#191364332
#191326332
#191326312
C43×#13732
#1243843