Finite Group Databasebeta

← #27173053

Subgroups — #27173053

Order 12928.

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

normal subgroups only

This group has 230 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
1C2×#15692277C211yesmaximal, characteristic, complemented
2C2×#15692199C211yesmaximal, characteristic, complemented
3C2×#15692196C211yesmaximal, characteristic, complemented
4#20264980C211yesmaximal, characteristic, complemented
5#20264977C211yesmaximal, characteristic, complemented
6C22⋊#13108049C211yesmaximal, characteristic, complemented
7#466×C101C211yesmaximal, characteristic, complemented
8C2×#13108074—21no—
9#15692277—22no—
10#15692277—22no—
11C2×Dic404C2211yescharacteristic
12C2×#13108063—21no—
13C2×D808C2211yescharacteristic
14#15692199—22no—
15#15692196—22no—
16C2×#13108049C2211yescharacteristic
17C2×#13108049C2211yescharacteristic
18C2×D8×C101C2211yescharacteristic
19C22×C8×C101C2211yescharacteristic
20#121×C101—21no—
21#107×C101C2211yescharacteristic
22#102×C101—21no—
23#13108074—24no—
24#13108074—42no—
25C2×Dic202—21no—
26C2×D404—21no—
27C2×C22⋊D101—41no—
28C2×C4×D101—41no—
29Dic404—21no—
30Dic404D412yescomplemented
31#13108063—24no—
32D808—21no—
33D808D412yescomplemented
34#13108049—21no—
35#13108049—21no—
36C2×D4×C101—21no—
37C2×D4×C101—41no—
38C22×C4×C101D411yescharacteristic
39D8×C101—21no—
40D8×C101—21no—
41C2×C8×C101—21no—
42C2×C8×C101—21no—
43C2×C8×C101D411yescharacteristic
44C2×C8×C101C2311yescharacteristic
45C4⋊C4×C101—21no—
46C22⋊C4×C101—41no—
47C23×C101—41no—
48C23×C101D811yescharacteristic
49C22×D101—41no—
50D4×C101—41no—
51D4×C101—41no—
52D4×C101—82no—
53C2×C4×C101—21no—
54C2×C4×C101—21no—
55C2×C4×C101—41no—
56C2×C4×C101D811yescharacteristic
57C2×C4×C101C2×D411yescharacteristic
58C22⋊D101—44no—
59C2×Dic101—41no—
60D404—22no—
61D404—41no—
62C4×D101—44no—
63Dic202—22no—
64Dic202—41no—
65C8×C101—21no—
66C8×C101C2×D411yescharacteristic
67C8×C101C2×D411yescharacteristic
68C22×C101—21no—
69C22×C101—21no—
70C22×C101—21no—
71C22×C101—81no—
72C22×C101—81no—
73C22×C101—81no—
74C22×C101C2×D811yescharacteristic
75C2×D101—42no—
76C2×D101—81no—
77C2×D101—81no—
78C4×C101—21no—
79C4×C101—81no—
80C4×C101#12011yescharacteristic
81C4×C101AGL(1,ℤ/8)11yescharacteristic
82Dic101—42no—
83C2×C101—41no—
84C2×C101—161no—
85C2×C101#44711yescharacteristic
86C2×C101#50811yescharacteristic
87C2×C101#50911yescharacteristic
88D101—82no—
89#2186—1011nomaximal, Sylow
90C101#218611yescharacteristic, complemented, Sylow
91C2×#135—1011no—
92C2×SD32—1011no—
93C2×D16—1011no—
94#466D10111yescharacteristic, complemented
95#358—1011no—
96#357—1011no—
97C22⋊C16—1011no—
98C2×#41—2021no—
99#135—2022no—
100#135—2022no—
101C2×Q16—1011no—
102C2×SD16—2021no—
103C2×D8—1011no—
104C2×D8C2×D10111yescharacteristic
105C22×C8C2×D10111yescharacteristic
106#121—21no—
107SD32—2022no—
108D16—2022no—
109C2×C16—1011no—
110C2×C16—1011no—
111#107C2×D10111yescharacteristic
112#102—21no—
113#41—4042no—
114#41—2024no—
115C2×Q8—2021no—
116C2×D4—21no—
117C2×D4—41no—
118C2×D4—4041no—
119C2×D4—2021no—
120C22×C4—4041no—
121C22×C4C22⋊D10111yescharacteristic
122Q16—1012no—
123Q16—2021no—
124SD16—2024no—
125D8—21no—
126D8—21no—
127D8—1012no—
128D8—2021no—
129C2×C8—21no—
130C2×C8—21no—
131C2×C8C22⋊D10111yescharacteristic
132C2×C8C22×D10111yescharacteristic
133C4⋊C4—21no—
134C22⋊C4—41no—
135C16—2021no—
136C16—2021no—
137C23—41no—
138C23—4041no—
139C23#1310805911yescharacteristic
140Q8—4041no—
141Q8—2022no—
142D4—41no—
143D4—41no—
144D4—82no—
145D4—4044no—
146D4—4041no—
147D4—2022no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—41no—
151C2×C4—4044no—
152C2×C4—4041no—
153C2×C4#1310805911yescharacteristic
154C2×C4C2×C22⋊D10111yescharacteristic
155C8—21no—
156C8D4×D10111yescharacteristic
157C8D4×D10111yescharacteristic
158C22—21no—
159C22—21no—
160C22—21no—
161C22—81no—
162C22—81no—
163C22—81no—
164C22—8081no—
165C22—8081no—
166C22—4042no—
167C22C2×#1310805911yescharacteristic
168C4—21no—
169C4—81no—
170C4—4042no—
171C4#1569222311yescharacteristic
172C4#1569228011yescharacteristic
173C2—41no—
174C2—161no—
175C2—8082no—
176C2#2026531011yescharacteristic
177C2#2026560711yescharacteristic
178C2#2026561311yescharacteristic
subgroupG/H
centerC22C2×#13108059
commutator, cosocleC2×C8×C101C23
FrattiniC2×C8C22×D101
Fitting#466×C101C2
socleC22×C101C2×D8
hypercenter#466D101
hypocenterC101#2186
LCSG ▷ C2×C8×C101 ▷ C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #466

Complements

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

NH ≅ G/Ntype
1. C2×#15692277C2semidirect
2. C2×#15692199C2semidirect
3. C2×#15692196C2semidirect
4. #20264980C2semidirect
5. #20264977C2semidirect
6. C22⋊#13108049C2semidirect
7. #466×C101C2semidirect
30. Dic404D4semidirect
33. D808D4semidirect
90. C101#2186semidirect
94. #466D101semidirect

Maximal subgroups

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

subgroupindex
C2×#156922772
C2×#156921992
C2×#156921962
#202649802
#202649772
C22⋊#131080492
#466×C1012
#2186101