Finite Group Databasebeta

← #24906555

Subgroups — #24906555

Order 10624.

256 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 55 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#19128356C211yesmaximal, characteristic, complemented
2#19128048C211yesmaximal, characteristic, complemented
3#19127897C211yesmaximal, characteristic, complemented
4#19127896C211yesmaximal, characteristic, complemented
5#19127448C211yesmaximal, characteristic, complemented
6#19127430C211yesmaximal, characteristic, complemented
7D4⋊C8×C83C211yesmaximal, characteristic, complemented
8C2×#13050590—21no—
9C2×D664—21no—
10C2×#13050575—21no—
11#14581792C2211yescharacteristic
12#14581789C2211yescharacteristic
13#14581774—22no—
14#14581771—21no—
15#14581763—21no—
16C4×D332C2211yescharacteristic
17C4⋊C4×D83—21no—
18C4⋊(C83⋊C8)C2211yescharacteristic
19#14581714—21no—
20#14581714—22no—
21#14581712—21no—
22C4×D4×C83C2211yescharacteristic
23C4⋊C8×C83C2211yescharacteristic
24C4×C8×C83C2211yescharacteristic
25#13050590—42no—
26#13050590—42no—
27C2×Dic166—21no—
28C2×D332—21no—
29C2×D332—21no—
30C2×D332—21no—
31C2×D332D411yescharacteristic
32C2×C22⋊D83—22no—
33C2×C4×D83—22no—
34C2×C4×D83—21no—
35D664—42no—
36#13050575—42no—
37C2×C83⋊C8—21no—
38C4⋊Dic83—21no—
39C4⋊Dic83D411yescharacteristic
40C4⋊Dic83D412yes—
41Dic83⋊C4—22no—
42C22⋊Dic83—22no—
43(C2×D83)⋊C4—21no—
44C2×D4×C83D411yescharacteristic
45C22×C4×C83—21no—
46C2×C8×C83—21no—
47C2×C8×C83—21no—
48C4⋊C4×C83D411yescharacteristic
49C22⋊C4×C83—21no—
50C42×C83C2311yescharacteristic
51C23×C83—21no—
52C22×D83—21no—
53C22×D83—41no—
54D4×C83—21no—
55D4×C83—21no—
56C2×C4×C83—21no—
57C2×C4×C83—41no—
58C2×C4×C83—41no—
59C2×C4×C83C2×D411yescharacteristic
60C2×C4×C83C2×D411yescharacteristic
61C2×C4×C83C2×D411yescharacteristic
62C22⋊D83—44no—
63C2×Dic83—21no—
64C2×Dic83—22no—
65D332—21no—
66D332—42no—
67D332—41no—
68D332—41no—
69D332—41no—
70D332—41no—
71D332D812yescomplemented
72C4×D83—44no—
73C4×D83—41no—
74C4×D83—41no—
75Dic166—41no—
76Dic166—41no—
77C8×C83—41no—
78C8×C83—41no—
79C83⋊C8—41no—
80C22×C83—41no—
81C22×C83—41no—
82C22×C83—41no—
83C22×C83#12011yescharacteristic
84C2×D83—22no—
85C2×D83—41no—
86C2×D83—41no—
87C2×D83—81no—
88C2×D83—81no—
89C2×D83—81no—
90C4×C83—21no—
91C4×C83—41no—
92C4×C83C2×D811yescharacteristic
93C4×C83#13511yescharacteristic
94C4×C83AGL(1,ℤ/8)11yescharacteristic
95C4×C83AGL(1,ℤ/8)11yescharacteristic
96Dic83—42no—
97Dic83—41no—
98C2×C83—81no—
99C2×C83#44711yescharacteristic
100C2×C83#44911yescharacteristic
101C2×C83#45411yescharacteristic
102D83—42no—
103D83—161no—
104#1625—831nomaximal, Sylow
105C83#162511yescharacteristic, complemented, Sylow
106#547—831no—
107#486—831no—
108#459—831no—
109#459—831no—
110#332—831no—
111D4⋊C8—831no—
112D4⋊C8D8311yescharacteristic, complemented
113C2×#41—1661no—
114C2×D8—1661no—
115C2×D8—1661no—
116C4⋊Q8—831no—
117#127—831no—
118#123—1662no—
119C22⋊Q8—1661no—
120#121—1661no—
121C4×D4—831no—
122C4×D4C2×D8311yescharacteristic
123C2×C4⋊C4—1661no—
124C4⋊C8—831no—
125C4⋊C8C2×D8311yescharacteristic
126#102—1661no—
127#102—1662no—
128#102—1661no—
129C4×C8C2×D8311yescharacteristic
130#41—3322no—
131#41—3322no—
132C2×Q8—1661no—
133C2×D4—831no—
134C2×D4—1662no—
135C2×D4—1661no—
136C2×D4—1661no—
137C2×D4—1661no—
138C2×D4D33211yescharacteristic
139C22×C4—21no—
140C22×C4—1662no—
141C22×C4—1661no—
142D8—3322no—
143D8—3322no—
144C2×C8—21no—
145C2×C8—21no—
146C2×C8—1661no—
147C4⋊C4—831no—
148C4⋊C4—832no—
149C4⋊C4—1662no—
150C4⋊C4—1661no—
151C4⋊C4D33211yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—1662no—
154C22⋊C4—1661no—
155C42C22×D8311yescharacteristic
156C23—21no—
157C23—3321no—
158C23—1661no—
159Q8—3321no—
160Q8—3321no—
161D4—21no—
162D4—21no—
163D4—3322no—
164D4—3324no—
165D4—3321no—
166D4—3321no—
167D4—3321no—
168D4—3321no—
169D4—832no—
170D4—1661no—
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—3324no—
175C2×C4—3321no—
176C2×C4—3321no—
177C2×C4—1661no—
178C2×C4—1662no—
179C2×C4D4×D8311yescharacteristic
180C2×C4D4×D8311yescharacteristic
181C2×C4C2×D33211yescharacteristic
182C8—41no—
183C8—41no—
184C8—3321no—
185C22—41no—
186C22—41no—
187C22—41no—
188C22—3321no—
189C22—3321no—
190C22—6641no—
191C22—6641no—
192C22—6641no—
193C22—1662no—
194C22#1458176211yescharacteristic
195C4—21no—
196C4—41no—
197C4—3322no—
198C4—3321no—
199C4D8×D8311yescharacteristic
200C4#1458181411yescharacteristic
201C4#1458181911yescharacteristic
202C4#1458182011yescharacteristic
203C2—81no—
204C2—13281no—
205C2—3322no—
206C2#1912783611yescharacteristic
207C2#1912784811yescharacteristic
208C2#1912787511yescharacteristic
subgroupG/H
centerC22#14581762
commutator, cosocleC42×C83C23
FrattiniC42C22×D83
FittingD4⋊C8×C83C2
socleC22×C83#120
hypercenterD4⋊C8D83
hypocenterC83#1625
LCSG ▷ C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
1. #19128356C2semidirect
2. #19128048C2semidirect
3. #19127897C2semidirect
4. #19127896C2semidirect
5. #19127448C2semidirect
6. #19127430C2semidirect
7. D4⋊C8×C83C2semidirect
71. D332D8semidirect
105. C83#1625semidirect
112. D4⋊C8D83semidirect

Maximal subgroups

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

subgroupindex
#191283562
#191280482
#191278972
#191278962
#191274482
#191274302
D4⋊C8×C832
#162583