Finite Group Databasebeta

← #24909154

Subgroups — #24909154

Order 10624.

262 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 65 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#19128265C211yesmaximal, characteristic
2#19127685C211yesmaximal, characteristic, complemented
3#19127497C214yesmaximal, complemented
4#413×C83C211yesmaximal, characteristic, complemented
5C22×D332C411yescharacteristic
6C2×#13050574—21no—
7#14581788C412yes—
8#14581781C2212yes—
9#14581766—21no—
10#14581766—21no—
11#14581760—21no—
12#14581760—21no—
13#14581751C411yescharacteristic
14#14581711C2212yescomplemented
15#14581709—21no—
16C2×#41×C83C2211yescharacteristic
17C2×M16×C83—21no—
18#101×C83C2212yescomplemented
19#100×C83—21no—
20C23×D83—21no—
21C2×D332—21no—
22C2×D332—41no—
23C2×D332—41no—
24C2×D332C2×C412yes—
25C2×C22⋊D83—22no—
26C2×C22⋊D83—22no—
27#13050574—22no—
28#13050574—41no—
29C2×C83⋊C8—41no—
30C4⋊Dic83—21no—
31C22⋊Dic83—21no—
32(C2×D83)⋊C4—22no—
33(C2×D83)⋊C4—22no—
34C4×Dic83C2×C412yes—
35#41×C83—41no—
36#41×C83—41no—
37C2×Q8×C83C2311yescharacteristic
38C2×D4×C83C2×C411yescharacteristic
39C2×D4×C83D411yescharacteristic
40C2×D4×C83D411yescharacteristic
41C22×C4×C83C2×C411yescharacteristic
42C22×C4×C83D411yescharacteristic
43C22×C4×C83D411yescharacteristic
44M16×C83—22no—
45M16×C83—41no—
46C2×C8×C83—41no—
47C23×C83C22⋊C411yescharacteristic
48C23×C83C22⋊C411yescharacteristic
49C23×C83C22⋊C411yescharacteristic
50C22×D83—22no—
51C22×D83—42no—
52C22×D83—82no—
53Q8×C83—41no—
54D4×C83—41no—
55D4×C83—41no—
56D4×C83—41no—
57C2×C4×C83—21no—
58C2×C4×C83—21no—
59C2×C4×C83—21no—
60C2×C4×C83—21no—
61C2×C4×C83—21no—
62C2×C4×C83—21no—
63C2×C4×C83C22⋊C411yescharacteristic
64C2×C4×C83C22×C411yescharacteristic
65C2×C4×C83C2×D411yescharacteristic
66C2×C4×C83C2×D411yescharacteristic
67C22⋊D83—82no—
68C22⋊D83—82no—
69C2×Dic83—22no—
70D332—42no—
71D332—41no—
72D332—41no—
73C8×C83—42no—
74C83⋊C8—42no—
75C22×C83—21no—
76C22×C83—21no—
77C22×C83—21no—
78C22×C83—41no—
79C22×C83—41no—
80C22×C83—41no—
81C22×C83C2×C22⋊C411yescharacteristic
82C2×D83—42no—
83C2×D83—42no—
84C2×D83—42no—
85C2×D83—84no—
86C4×C83—21no—
87C4×C83—21no—
88C4×C83—21no—
89C4×C83#9911yescharacteristic
90C4×C83#9911yescharacteristic
91Dic83—42no—
92C2×C83—21no—
93C2×C83—41no—
94C2×C83—41no—
95C2×C83—41no—
96C2×C83C2×#9911yescharacteristic
97D83—82no—
98#2134—831nomaximal, Sylow
99C83#213411yescharacteristic, complemented, Sylow
100#535—831no—
101#413—831no—
102#413D8311yescharacteristic, complemented
103#355—834no—
104C2×#41C2×D8311yescharacteristic
105C22×D4—831no—
106C2×M16—21no—
107C2×M16—1661no—
108#127—832no—
109#124—832no—
110#121—1661no—
111#121—1661no—
112#120—1661no—
113#120—1661no—
114#117—831no—
115#101—832no—
116#101C2×D8312yescomplemented
117#100—21no—
118#100—1661no—
119C24—1661no—
120#41—41no—
121#41—41no—
122C2×Q8C22×D8311yescharacteristic
123C2×D4—3321no—
124C2×D4—3321no—
125C2×D4—832no—
126C2×D4—1662no—
127C2×D4—1662no—
128C2×D4—1661no—
129C2×D4C4×D8311yescharacteristic
130C2×D4D33211yescharacteristic
131C2×D4C22⋊D8311yescharacteristic
132C22×C4C4×D8311yescharacteristic
133C22×C4D33211yescharacteristic
134C22×C4C22⋊D8311yescharacteristic
135M16—22no—
136M16—41no—
137M16—3321no—
138M16—1662no—
139C2×C8—41no—
140C2×C8—3321no—
141C4⋊C4—1661no—
142C22⋊C4—1661no—
143C22⋊C4—1662no—
144C22⋊C4—1662no—
145C42—832no—
146C23—3322no—
147C23—6642no—
148C23—1662no—
149C23(C2×D83)⋊C411yescharacteristic
150C23(C2×D83)⋊C411yescharacteristic
151C23(C2×D83)⋊C411yescharacteristic
152Q8—41no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—3322no—
157D4—3321no—
158D4—3321no—
159D4—6642no—
160D4—6642no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—1662no—
168C2×C4(C2×D83)⋊C411yescharacteristic
169C2×C4C2×C4×D8311yescharacteristic
170C2×C4C2×C22⋊D8311yescharacteristic
171C2×C4C2×D33211yescharacteristic
172C8—42no—
173C8—3322no—
174C22—21no—
175C22—21no—
176C22—21no—
177C22—41no—
178C22—41no—
179C22—41no—
180C22—3322no—
181C22—3322no—
182C22—3322no—
183C22—6644no—
184C22C2×(C2×D83)⋊C411yescharacteristic
185C4—21no—
186C4—21no—
187C4—21no—
188C4—3322no—
189C4#1458170611yescharacteristic
190C4#1458170611yescharacteristic
191C2—21no—
192C2—41no—
193C2—41no—
194C2—41no—
195C2—6642no—
196C2C2×#1458170611yescharacteristic
subgroupG/H
centerC2C2×#14581706
commutatorC2×C4×C83C22×C4
FrattiniC2×Q8C22×D83
Fitting#413×C83C2
socleC2×C83C2×#99
prime radical#19128265C2
cosocleC2×Q8×C83C23
hypercenter#413D83
hypocenterC83#2134
LCSG ▷ C2×C4×C83 ▷ C22×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #413

Complements

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

NH ≅ G/Ntype
2. #19127685C2semidirect
3. #19127497C2semidirect
4. #413×C83C2semidirect
14. #14581711C22semidirect
18. #101×C83C22semidirect
99. C83#2134semidirect
102. #413D83semidirect
116. #101C2×D83semidirect

Maximal subgroups

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

subgroupindex
#191282652
#191276852
#191274972
#413×C832
#213483