Finite Group Databasebeta

← C2×#10593388 #11874960

Subgroups — C2×#10593388 #11874960

Order 1152.

714 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 714 conjugacy classes of subgroups — too many to draw. Only its 159 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×#63873C212yesmaximal
2C2×C4×#622C211yesmaximal, characteristic
3C2×#63743C214yesmaximal
4#10593388C218yesmaximal, direct product factor
5C22×C3×Dic6—22no—
6C22×#622C2212yes—
7C2×C4×C3⋊Dic3C2211yescharacteristic
8C2×#3724—22no—
9C2×#3724C2214yes—
10#63873—24no—
11#63873C2218yes—
12C4×#622C2214yes—
13#63743C22116yes—
14C2×#944—62no—
15C22×C32×C4D411yescharacteristic
16C22×C3⋊Dic3D411yescharacteristic
17C22×C3⋊Dic3C2311yescharacteristic
18C22×C3×Dic3—24no—
19C2×C3×Dic6—28no—
20C2×C3×Dic6—48no—
21C2×#622Q818yescomplemented
22C2×#622C2314yes—
23C4×C3⋊Dic3D412yes—
24C4×C3⋊Dic3C2312yes—
25#3724—24no—
26#3724—28no—
27#3724C2318yes—
28C2×#500—91nomaximal, Sylow
29C22×C3×Q8—62no—
30C22×Dic6—22no—
31#944—68no—
32#944—68no—
33C2×Dic3⋊C4—64no—
34C2×Dic3⋊C4—64no—
35C2×C4×Dic3—62no—
36C23×C32C2×D411yescharacteristic
37C2×C32×C4D814yes—
38C2×C32×C4C2×D412yes—
39C2×C3⋊Dic3Q1614yes—
40C2×C3⋊Dic3C2×D411yescharacteristic
41C2×C3⋊Dic3C2×D412yes—
42C2×C3⋊Dic3C2×Q814yes—
43C2×C3⋊Dic3C2411yescharacteristic
44C2×C3×Dic3—28no—
45C2×C3×Dic3—48no—
46C3×Dic6—416no—
47#622C2×Q818yescomplemented
48C2×C4⋊Q8—92no—
49#500—98no—
50C2×#107—94no—
51C2×C4×C8—91no—
52C2×C3×Q8—68no—
53C2×C3×Q8—128no—
54C22×C3×C4—22no—
55C22×C3×C4—64no—
56C22×Dic3—24no—
57C22×Dic3—62no—
58C22×Dic3—62no—
59C2×Dic6—28no—
60C2×Dic6—48no—
61Dic3⋊C4—68no—
62Dic3⋊C4—68no—
63Dic3⋊C4—616no—
64C4×Dic3—64no—
65C4×Dic3—64no—
66C22×C32C4⋊Q812yes—
67C22×C32C2×D812yes—
68C22×C32C2×Q1612yes—
69C22×C32C22×D411yescharacteristic
70C32×C4C2×D814yes—
71C3⋊Dic3C4⋊Q812yes—
72C3⋊Dic3C2×Q1614yes—
73C3⋊Dic3C22×Q812yes—
74C3×Dic3—48no—
75C22×Q8—62no—
76C22×C8—92no—
77C4⋊Q8—98no—
78C4⋊Q8—184no—
79C2×C4⋊C4—94no—
80C2×C4⋊C4—182no—
81C2×C42—91no—
82#107—916no—
83C4×C8—94no—
84C23×C3—22no—
85C3×Q8—1216no—
86C2×C3×C4—24no—
87C2×C3×C4—28no—
88C2×C3×C4—68no—
89C2×C3×C4—128no—
90C2×Dic3—28no—
91C2×Dic3—48no—
92C2×Dic3—68no—
93C2×Dic3—62no—
94C2×Dic3—64no—
95C2×Dic3—68no—
96C2×Dic3—62no—
97Dic6—416no—
98C2×C32#50014yescomplemented
99C2×C32C2×C4⋊Q811yescharacteristic
100C2×C32C22×D811yescharacteristic
101C2×C32C22×Q1611yescharacteristic
102C2×Q8—68no—
103C2×Q8—128no—
104C22×C4—64no—
105C22×C4—91no—
106C22×C4—91no—
107C22×C4GO+(4,𝔽2)11yescharacteristic
108C2×C8—94no—
109C2×C8—98no—
110C4⋊C4—98no—
111C4⋊C4—184no—
112C4⋊C4—188no—
113C42—92no—
114C42—92no—
115C22×C3—22no—
116C22×C3—24no—
117C22×C3—24no—
118C22×C3—24no—
119C3×C4—28no—
120C3×C4—128no—
121Dic3—48no—
122Dic3—64no—
123Dic3—68no—
124Dic3—64no—
125C32C2×#50011yescharacteristic, complemented, Sylow
126C23C2×GO+(4,𝔽2)11yescharacteristic
127Q8—1216no—
128C2×C4—68no—
129C2×C4—91no—
130C2×C4—91no—
131C2×C4—92no—
132C2×C4—94no—
133C2×C4—94no—
134C2×C4—128no—
135C2×C4#377414yes—
136C2×C4C2×GO+(4,𝔽2)12yes—
137C8—98no—
138C2×C3—28no—
139C2×C3—22no—
140C2×C3—22no—
141C2×C3—22no—
142C22#6422212yes—
143C22#6422812yes—
144C22C2×#377412yes—
145C22C22×GO+(4,𝔽2)11yescharacteristic
146C4—92no—
147C4—92no—
148C4—94no—
149C4—128no—
150C4C2×#377414yes—
151C3—22no—
152C2#1059338814yesdirect product factor
153C2C2×#6422211yescharacteristic
154C2C2×#6422811yescharacteristic
155C2C22×#377411yescharacteristic
subgroupG/H
centerC23C2×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FrattiniC22C22×GO+(4,𝔽2)
FittingC22×C32×C4D4
socle, prime radicalC23×C32C2×D4
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#500
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #10593388C2direct (N × H)
21. C2×#622Q8semidirect
47. #622C2×Q8semidirect
98. C2×C32#500semidirect
125. C32C2×#500semidirect
152. C2#10593388direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#638732
C2×C4×#6222
C2×#637432
#105933882
C2×#5009