Finite Group Databasebeta

← #27170405

Subgroups — #27170405

Order 12928.

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#20265897C211yesmaximal, characteristic
2#20265575C211yesmaximal, characteristic, complemented
3#20265457C211yesmaximal, characteristic
4#20265388C211yesmaximal, characteristic, complemented
5#20264922C211yesmaximal, characteristic, complemented
6#20264909C211yesmaximal, characteristic, complemented
7D4⋊C8×C101C211yesmaximal, characteristic
8C2×Dic404—21no—
9#15692255C2211yescharacteristic
10#15692255C2211yescharacteristic
11#15692248—22no—
12#15692242—21no—
13#15692234—21no—
14C4×Dic202C2211yescharacteristic
15#15692220—21no—
16#15692214—21no—
17#15692188—21no—
18#15692187—22no—
19C4⋊#11717579C2211yescharacteristic
20#15692180—21no—
21#15692176—21no—
22C4×D4×C101C2211yescharacteristic
23C4⋊C8×C101C2211yescharacteristic
24C4×C8×C101C2211yescharacteristic
25C2×Dic202—21no—
26C2×Dic202—21no—
27C2×Dic202D411yescharacteristic
28Dic404—42no—
29C2×#11717579—21no—
30C4⋊Dic101—21no—
31C4⋊Dic101—21no—
32C4⋊Dic101—21no—
33C4⋊Dic101D411yescharacteristic
34C4⋊Dic101D412yes—
35#13108053—22no—
36#13108053—21no—
37C22⋊Dic101—22no—
38C22⋊Dic101—22no—
39C4×Dic101—22no—
40C4×Dic101—21no—
41C2×D4×C101D411yescharacteristic
42C22×C4×C101—21no—
43C2×C8×C101—21no—
44C2×C8×C101—21no—
45C4⋊C4×C101D411yescharacteristic
46C22⋊C4×C101—21no—
47C42×C101C2311yescharacteristic
48C23×C101—21no—
49D4×C101—21no—
50D4×C101—21no—
51C2×C4×C101—21no—
52C2×C4×C101—41no—
53C2×C4×C101—41no—
54C2×C4×C101C2×D411yescharacteristic
55C2×C4×C101C2×D411yescharacteristic
56C2×C4×C101C2×D411yescharacteristic
57C2×Dic101—21no—
58C2×Dic101—21no—
59C2×Dic101—22no—
60C2×Dic101—41no—
61Dic202—21no—
62Dic202—21no—
63Dic202—41no—
64Dic202—41no—
65Dic202—41no—
66Dic202—41no—
67C8×C101—22no—
68C8×C101—41no—
69#11717579—41no—
70C22×C101—41no—
71C22×C101—41no—
72C22×C101—41no—
73C22×C101#12011yescharacteristic
74C4×C101—21no—
75C4×C101—41no—
76C4×C101#13511yescharacteristic
77C4×C101#13511yescharacteristic
78C4×C101AGL(1,ℤ/8)11yescharacteristic
79C4×C101#13711yescharacteristic
80Dic101—41no—
81Dic101—42no—
82Dic101—41no—
83Dic101—81no—
84C2×C101—81no—
85C2×C101#44911yescharacteristic
86C2×C101#45211yescharacteristic
87C2×C101#45611yescharacteristic
88#1652—1011nomaximal, Sylow
89C101#165211yescharacteristic, complemented, Sylow
90#556—1011no—
91#498—1011no—
92#474—1011no—
93#462—1011no—
94#332—1011no—
95Q8⋊C8—1011no—
96D4⋊C8D10111yescharacteristic
97C2×Q16—2021no—
98C4⋊Q8—1011no—
99C4⋊Q8—1011no—
100#126—2022no—
101#124—2021no—
102C22⋊Q8—2021no—
103C4×Q8—1011no—
104C4×Q8—2021no—
105C4×D4C2×D10111yescharacteristic
106#117—2021no—
107#107—2021no—
108#106—2022no—
109C4⋊C8—1011no—
110C4⋊C8C2×D10111yescharacteristic
111#103—2021no—
112#102—2021no—
113C4×C8C2×D10111yescharacteristic
114C2×Q8—1011no—
115C2×Q8—2021no—
116C2×Q8—2021no—
117C2×D4D40411yescharacteristic
118C22×C4—21no—
119Q16—4042no—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—2021no—
123C4⋊C4—1011no—
124C4⋊C4—1012no—
125C4⋊C4—2022no—
126C4⋊C4—2021no—
127C4⋊C4—2021no—
128C4⋊C4—2021no—
129C4⋊C4—2021no—
130C4⋊C4D40411yescharacteristic
131C22⋊C4—21no—
132C22⋊C4—2022no—
133C22⋊C4—2022no—
134C42—2022no—
135C42—2021no—
136C42C22×D10111yescharacteristic
137C23—21no—
138Q8—4041no—
139Q8—4041no—
140Q8—4041no—
141Q8—4041no—
142Q8—2021no—
143Q8—2021no—
144D4—21no—
145D4—21no—
146C2×C4—21no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—4041no—
150C2×C4—2021no—
151C2×C4—2022no—
152C2×C4—2021no—
153C2×C4D4×D10111yescharacteristic
154C2×C4D4×D10111yescharacteristic
155C2×C4C2×D40411yescharacteristic
156C8—22no—
157C8—41no—
158C8—4041no—
159C22—41no—
160C22—41no—
161C22—41no—
162C22#1569222511yescharacteristic
163C4—21no—
164C4—41no—
165C4—8081no—
166C4—4041no—
167C4—4042no—
168C4—4041no—
169C4#1569227611yescharacteristic
170C4#1569227711yescharacteristic
171C4#1569227911yescharacteristic
172C4#1569228811yescharacteristic
173C2—81no—
174C2#2026532311yescharacteristic
175C2#2026534111yescharacteristic
176C2#2026536111yescharacteristic
subgroupG/H
centerC22#15692225
commutator, cosocleC42×C101C23
FrattiniC42C22×D101
FittingD4⋊C8×C101C2
socleC22×C101#120
prime radicalC2×D4×C101D4
hypercenterD4⋊C8D101
hypocenterC101#1652
LCSG ▷ C42×C101 ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #20265575C2semidirect
4. #20265388C2semidirect
5. #20264922C2semidirect
6. #20264909C2semidirect
89. C101#1652semidirect

Maximal subgroups

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

subgroupindex
#202658972
#202655752
#202654572
#202653882
#202649222
#202649092
D4⋊C8×C1012
#1652101