Finite Group Databasebeta

← #25085923

Subgroups — #25085923

Order 11008.

736 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 736 conjugacy classes of subgroups — too many to draw. Only its 151 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#19145339C213yesmaximal, complemented
2#19144966C213yesmaximal
3#19134256C213yesmaximal, complemented
4#19134252C213yesmaximal, complemented
5#19134207C211yesmaximal, characteristic, complemented
6#19132897C211yesmaximal, characteristic, complemented
7C43×#1711C211yesmaximal, characteristic, complemented
8#14583454C2213yes—
9#127×D43C2211yescharacteristic
10#14583295C2213yescomplemented
11#14583278C2213yescomplemented
12#14583262—26no—
13#14583250C2213yescomplemented
14#14583247C2213yes—
15#14583246C2213yes—
16#14583245C2213yes—
17#14583156—26no—
18#14583003—26no—
19#14582902—26no—
20C4×#10621872C2213yes—
21#14582620C2213yescomplemented
22C43×#487C2213yescomplemented
23C43×#486C2213yes—
24C82×C43C2211yescharacteristic, complemented
25C2×D4×D43—23no—
26C2×#10621885—26no—
27C2×#10621872D416yes—
28#13063325C2313yes—
29#13063322C2311yescharacteristic
30#13063321—23no—
31#13063316—23no—
32#13063305—23no—
33#13063301—23no—
34Q8×Dic43—23no—
35#13063290—23no—
36#13063283—23no—
37C42×D43C2311yescharacteristic
38#13063256—26no—
39#13063250—26no—
40#13063247—26no—
41#13063246—26no—
42#13063245—26no—
43#13063235D416yes—
44C4×C43⋊C8C2313yes—
45C4⋊Q8×C43C2313yes—
46#127×C43C2311yescharacteristic
47#103×C43—26no—
48#102×C43—26no—
49C4×C8×C43C2313yes—
50C23×D43—41no—
51C2×Q8×C43—23no—
52C2×D4×C43—23no—
53C2×C22⋊D43—43no—
54D4×D43—412no—
55C2×D172—23no—
56C2×C4×D43C2×D413yes—
57C2×Dic86—23no—
58C2×C8×C43C2×D416yes—
59C4⋊C4×C43—23no—
60C4⋊C4×C43—23no—
61C42×C43C2411yescharacteristic
62#10621885—412no—
63(C2×D43)⋊C4—43no—
64C4⋊Dic43—23no—
65C4⋊Dic43—23no—
66C4⋊Dic43—43no—
67Dic43⋊C4—43no—
68C4×Dic43—43no—
69C4×Dic43C2×D413yes—
70C2×C43⋊C8C2×D416yes—
71#10621872—46no—
72C23×C43—41no—
73C22×D43—41no—
74C22×D43—86no—
75C22×D43#12711yescharacteristic
76Q8×C43—46no—
77D4×C43—46no—
78C2×C4×C43—43no—
79C2×C4×C43C22×D413yes—
80C22⋊D43—86no—
81C2×Dic43—43no—
82C2×Dic43#12713yes—
83D172—46no—
84C4×D43—26no—
85Dic86—46no—
86C8×C43—26no—
87C43⋊C8—26no—
88#19753—431nomaximal, Sylow
89C22×C43—83no—
90C22×C43C2×#12711yescharacteristic
91C2×D43—23no—
92C2×D43—83no—
93C2×D43—164no—
94C4×C43—83no—
95C4×C43#57516yes—
96Dic43—23no—
97Dic43—83no—
98#3185—433no—
99#3138—433no—
100#1720—433no—
101#1720—433no—
102#1711—431no—
103#1711D4311yescharacteristic, complemented
104#1455—431no—
105C2×C43—161no—
106C2×C43#315313yes—
107D43—41no—
108D43—161no—
109#533—433no—
110C2×#127—431no—
111#498—433no—
112#494—433no—
113#490—866no—
114#487—433no—
115#487C2×D4313yescomplemented
116#486—433no—
117#486—433no—
118#486—433no—
119#486C2×D4313yes—
120#470—866no—
121#441—866no—
122#418—866no—
123C4×M16—433no—
124#322—433no—
125C82C2×D4311yescharacteristic, complemented
126C43#1975311yescharacteristic, complemented, Sylow
127C22×D4—863no—
128C2×Q16—866no—
129C2×M16—436no—
130C4⋊Q8—433no—
131C4⋊Q8C22×D4313yes—
132#127—431no—
133#127—863no—
134#127C22×D4311yescharacteristic
135#125—863no—
136C22⋊Q8—863no—
137C22⋊Q8—863no—
138C4×Q8—863no—
139C4×Q8—863no—
140#117—863no—
141C2×C42—431no—
142#106—866no—
143#103—26no—
144#103—866no—
145#102—26no—
146#102—866no—
147#102—866no—
148#102—866no—
149#97—436no—
150C4×C8—433no—
151C4×C8C22×D4313yes—
152C24—1721no—
153C2×Q8—23no—
154C2×Q8—863no—
155C2×D4—23no—
156C2×D4—863no—
157C2×D4—1723no—
158C2×D4—17212no—
159C22×C4—433no—
160Q16—17212no—
161M16—1726no—
162C2×C8—436no—
163C2×C8D4×D4316yes—
164C4⋊C4—23no—
165C4⋊C4—23no—
166C4⋊C4—863no—
167C4⋊C4—863no—
168C4⋊C4—1723no—
169C4⋊C4—1723no—
170C22⋊C4—1723no—
171C42—433no—
172C42—1723no—
173C42C23×D4311yescharacteristic
174C23—41no—
175C23—431no—
176C23—3446no—
177C23—1721no—
178Q8—46no—
179Q8—1726no—
180D4—46no—
181D4—3446no—
182D4—1726no—
183C2×C4—43no—
184C2×C4—433no—
185C2×C4—866no—
186C2×C4—1723no—
187C2×C4C2×D4×D4313yes—
188C8—26no—
189C8—866no—
190C22—83no—
191C22—863no—
192C22—3443no—
193C22—6884no—
194C22#127×D4311yescharacteristic
195C4—83no—
196C4—863no—
197C4—3443no—
198C4#1458369616yes—
199C2—161no—
200C2—1721no—
201C2—6881no—
202C2#1914505613yes—
subgroupG/H
centerC22#127×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1711C2
socleC22×C43C2×#127
prime radical#127×D43C22
hypercenter#1711D43
hypocenterC43#19753
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1711

Complements

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

NH ≅ G/Ntype
1. #19145339C2semidirect
3. #19134256C2semidirect
4. #19134252C2semidirect
5. #19134207C2semidirect
6. #19132897C2semidirect
7. C43×#1711C2semidirect
10. #14583295C22semidirect
11. #14583278C22semidirect
13. #14583250C22semidirect
21. #14582620C22semidirect
22. C43×#487C22semidirect
24. C82×C43C22semidirect
103. #1711D43semidirect
115. #487C2×D43semidirect
125. C82C2×D43semidirect
126. C43#19753semidirect

Maximal subgroups

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

subgroupindex
#191453392
#191449662
#191342562
#191342522
#191342072
#191328972
C43×#17112
#1975343