Finite Group Databasebeta

← #35325220

Subgroups — #35325220

Order 21248.

200 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 53 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#24909775C211yesmaximal, characteristic
2#24909725C211yesmaximal, characteristic, complemented
3#24909344C211yesmaximal, characteristic, complemented
4#24905660C211yesmaximal, characteristic, complemented
5#24905656C211yesmaximal, characteristic, complemented
6#24905654C211yesmaximal, characteristic, complemented
7C83×#2264C211yesmaximal, characteristic, complemented
8C2×#14581735—21no—
9C2×D1328C2211yescharacteristic
10#19128086—21no—
11#19127818—21no—
12#19127538—21no—
13#19127536—21no—
14#19127535C2211yescharacteristic
15#19127531C2211yescharacteristic
16#19127508—21no—
17C16×Dic83C2211yescharacteristic
18#508×C83C2211yescharacteristic
19C2×Q32×C83C2211yescharacteristic
20Q64×C83—21no—
21SD64×C83—21no—
22M64×C83C2211yescharacteristic
23C2×#13050577—41no—
24C2×D664—21no—
25#14581799—41no—
26#14581781—41no—
27#14581735—42no—
28D1328—21no—
29D1328—21no—
30C2×C83⋊C16D411yescharacteristic
31#14581728—21no—
32#14581719—41no—
33C8×Dic83D411yescharacteristic
34C83⋊C32—21no—
35#135×C83—21no—
36C2×Q16×C83—21no—
37Q32×C83—21no—
38Q32×C83—21no—
39Q32×C83D411yescharacteristic
40SD32×C83—21no—
41D16×C83D411yescharacteristic
42C2×C16×C83C2311yescharacteristic
43C32×C83—21no—
44C2×D332—41no—
45#13050577—81no—
46#13050577—81no—
47D664—41no—
48D664—41no—
49#13050574—41no—
50#13050574—81no—
51C2×C83⋊C8—81no—
52C2×C83⋊C8D811yescharacteristic
53(C2×D83)⋊C4—82no—
54C4×Dic83D811yescharacteristic
55C83⋊C16—21no—
56#41×C83—41no—
57C2×Q8×C83—41no—
58Q16×C83—21no—
59Q16×C83—41no—
60Q16×C83—41no—
61SD16×C83—41no—
62D8×C83—21no—
63C2×C8×C83C2×D411yescharacteristic
64C16×C83C2×D411yescharacteristic
65C16×C83#4111yescharacteristic
66C22×D83—81no—
67Q8×C83—41no—
68Q8×C83—81no—
69Q8×C83—81no—
70D4×C83—41no—
71D4×C83—81no—
72C2×C4×C83—81no—
73C2×C4×C83—81no—
74C2×C4×C83C2×D811yescharacteristic
75C2×Dic83—21no—
76D332—81no—
77D332—81no—
78C8×C83#12111yescharacteristic
79C8×C83AGL(1,ℤ/8)11yescharacteristic
80C83⋊C8—81no—
81C83⋊C8D1611yescharacteristic
82C83⋊C8D1611yescharacteristic
83C22×C83—81no—
84C22×C83#50911yescharacteristic
85C2×D83—162no—
86C2×D83—161no—
87C4×C83—81no—
88C4×C83—161no—
89C4×C83#45911yescharacteristic
90C4×C83C2×D1611yescharacteristic
91Dic83—41no—
92#13691—831nomaximal, Sylow
93C2×C83—21no—
94C2×C83—161no—
95C2×C83#220611yescharacteristic
96D83—321no—
97#2264D8311yescharacteristic, complemented
98#2263—831no—
99#2249—831no—
100#2178—831no—
101#1422—831no—
102#1420—831no—
103#1419—831no—
104C83#1369111yescharacteristic, complemented, Sylow
105#508C2×D8311yescharacteristic
106C2×Q32C2×D8311yescharacteristic
107C2×SD32—1661no—
108C2×D16—831no—
109#495—1661no—
110#443—1661no—
111Q64—21no—
112SD64—21no—
113SD64—1661no—
114D32—1661no—
115M64—831no—
116M64C2×D8311yescharacteristic
117#368—831no—
118#359—1661no—
119C4×C16—831no—
120#135—21no—
121C2×Q16—21no—
122C2×SD16—3321no—
123C2×D8—1661no—
124#131—3321no—
125#124—3321no—
126Q32—21no—
127Q32—21no—
128Q32C22⋊D8311yescharacteristic
129SD32—21no—
130SD32—3322no—
131D16—1661no—
132D16—1661no—
133D16C22⋊D8311yescharacteristic
134C2×C16—831no—
135C2×C16C22×D8311yescharacteristic
136#108—1661no—
137#104—3321no—
138C4×C8—831no—
139C32—21no—
140C32—1661no—
141#41—41no—
142C2×Q8—41no—
143C2×D4—3321no—
144Q16—21no—
145Q16—41no—
146Q16—41no—
147SD16—41no—
148SD16—6641no—
149SD16—6641no—
150D8—21no—
151D8—3321no—
152D8—3321no—
153M16—3321no—
154M16—6641no—
155C2×C8—831no—
156C2×C8—6641no—
157C2×C8D4×D8311yescharacteristic
158C22⋊C4—6642no—
159C42—831no—
160C16—1661no—
161C16C2×C22⋊D8311yescharacteristic
162C16#1305058911yescharacteristic
163C23—6641no—
164Q8—41no—
165Q8—81no—
166Q8—81no—
167D4—41no—
168D4—81no—
169D4—6641no—
170D4—6641no—
171C2×C4—81no—
172C2×C4—81no—
173C2×C4—1661no—
174C2×C4D8×D8311yescharacteristic
175C8—831no—
176C8—831no—
177C8—6641no—
178C8#1458176411yescharacteristic
179C8#1458181611yescharacteristic
180C22—81no—
181C22—13282no—
182C22—13281no—
183C22#1912813511yescharacteristic
184C4—81no—
185C4—161no—
186C4—3321no—
187C4#1912789411yescharacteristic
188C4D16×D8311yescharacteristic
189C2—21no—
190C2—161no—
191C2—26561no—
192C2#2490949611yescharacteristic
subgroupG/H
centerC2#24909496
commutator, cosocleC2×C16×C83C23
FrattiniC2×C16C22×D83
FittingC83×#2264C2
socleC2×C83#2206
prime radical#24909775C2
hypercenter#2264D83
hypocenterC83#13691
LCSG ▷ C2×C16×C83 ▷ C8×C83 ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #2264

Complements

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

NH ≅ G/Ntype
2. #24909725C2semidirect
3. #24909344C2semidirect
4. #24905660C2semidirect
5. #24905656C2semidirect
6. #24905654C2semidirect
7. C83×#2264C2semidirect
97. #2264D83semidirect
104. C83#13691semidirect

Maximal subgroups

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

subgroupindex
#249097752
#249097252
#249093442
#249056602
#249056562
#249056542
C83×#22642
#1369183