Finite Group Databasebeta

← #11790616

Subgroups — #11790616

Order 1152.

622 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 622 conjugacy classes of subgroups — too many to draw. Only its 98 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
1C3⋊D3×C4⋊Q8C211yesmaximal, characteristic
2C2×#63784C214yesmaximal
3#10593735C211yesmaximal, characteristic
4C4×#3787C211yesmaximal, characteristic
5C2×Q8×C3⋊D3C2212yes—
6C2×C4⋊#157—22no—
7C2×C4⋊#157C2212yes—
8C2×#3787C2212yes—
9C32×C4⋊Q8C411yescharacteristic, complemented
10#64153C412yescomplemented
11C4⋊C4×C3⋊D3—22no—
12#64097—22no—
13C42×C3⋊D3C2211yescharacteristic
14#64078C411yescharacteristic, complemented
15#63784—28no—
16C4×#622—22no—
17D3×C4⋊Q8—62no—
18C22×#157—22no—
19C2×C32×Q8C2×C412yes—
20Q8×C3⋊D3—24no—
21Q8×C3⋊D3—24no—
22C2×C4×C3⋊D3—22no—
23C2×C4×C3⋊D3D412yes—
24C2×C4×C3⋊D3C2311yescharacteristic
25C2×#634—22no—
26C2×#634C2×C412yes—
27C2×#622—22no—
28C4⋊#157—24no—
29C4⋊#157—44no—
30#3787—22no—
31#3787D414yes—
32C32×C4⋊C4—22no—
33C32×C42C2×C411yescharacteristic
34C4⋊(C3⋊Dic3)—22no—
35#3750—24no—
36C4×C3⋊Dic3C2×C411yescharacteristic
37C4×C3⋊Dic3D412yes—
38#1956—91nomaximal, Sylow
39C2×D3×Q8—64no—
40C3×C4⋊Q8—22no—
41#944—64no—
42D3×C4⋊C4—68no—
43#888—68no—
44C42×D3—62no—
45#869—62no—
46C22×C3⋊D3C2×D411yescharacteristic
47C2×#157—42no—
48C2×#157—44no—
49C32×Q8—24no—
50C2×C32×C4—22no—
51C2×C32×C4C22⋊C412yes—
52C2×C32×C4C22×C411yescharacteristic
53C2×C3⋊Dic3—22no—
54C2×C3⋊Dic3C22⋊C412yes—
55C2×C3⋊Dic3C2×D411yescharacteristic
56C4×C3⋊D3—42no—
57C4×C3⋊D3—42no—
58C4×C3⋊D3SD1614yes—
59C4×C3⋊D3Q1614yes—
60C4×C3⋊D3C2×D412yes—
61C4×C3⋊D3#4112yes—
62#634—24no—
63#634—44no—
64#622—24no—
65C2×C4⋊Q8—91no—
66C2×#103—94no—
67C2×C4×C8—91no—
68#384—91no—
69C2×C3×Q8—24no—
70D3×Q8—128no—
71D3×Q8—128no—
72C2×C4×D3—64no—
73C2×C4×D3—62no—
74C2×C4×D3—68no—
75C2×Dic6—64no—
76C2×Dic6—68no—
77C3×C4⋊C4—28no—
78C3×C42—22no—
79C4⋊Dic3—68no—
80Dic3⋊C4—616no—
81C4×Dic3—64no—
82C4×Dic3—62no—
83C22×C32C2×C22⋊C411yescharacteristic
84C2×C3⋊D3#12411yescharacteristic
85C2×C3⋊D3#12711yescharacteristic
86C2×C3⋊D3C2×SD1612yes—
87C2×C3⋊D3C2×Q1612yes—
88#157—82no—
89C32×C4—42no—
90C32×C4#10314yescomplemented
91C32×C4C4×D412yes—
92C3⋊Dic3—42no—
93C3⋊Dic3#10314yescomplemented
94C3⋊Dic3#12112yes—
95C22×Q8—92no—
96C22×C8—92no—
97C4⋊Q8—92no—
98C4⋊Q8—91no—
99C4⋊Q8—182no—
100C4⋊Q8#15711yescharacteristic, complemented
101C2×C4⋊C4—92no—
102C2×C4⋊C4—182no—
103C2×C4⋊C4—182no—
104C2×C42—91no—
105#103—188no—
106C4×C8—182no—
107C22×D3—62no—
108C3×Q8—48no—
109C2×C3×C4—28no—
110C2×C3×C4—22no—
111C2×C3×C4—24no—
112C2×Dic3—64no—
113C2×Dic3—62no—
114C2×Dic3—68no—
115C4×D3—68no—
116C4×D3—68no—
117C4×D3—64no—
118C4×D3—64no—
119C4×D3—128no—
120C4×D3—128no—
121Dic6—128no—
122Dic6—1216no—
123C2×C32#39011yescharacteristic
124C2×C32C2×#10312yes—
125C3⋊D3#48712yes—
126C3⋊D3#49211yescharacteristic
127C3⋊D3#49411yescharacteristic
128C2×Q8—92no—
129C2×Q8—182no—
130C2×Q8—184no—
131C2×Q8—184no—
132C2×Q8C2×#15712yes—
133C22×C4—91no—
134C22×C4—92no—
135C22×C4—182no—
136C22×C4—182no—
137C2×C8—94no—
138C2×C8—182no—
139C2×C8—182no—
140C4⋊C4—22no—
141C4⋊C4—184no—
142C4⋊C4—184no—
143C4⋊C4—182no—
144C4⋊C4—364no—
145C42—91no—
146C42—92no—
147C42C2×#15711yescharacteristic
148C22×C3—22no—
149C2×D3—62no—
150C2×D3—62no—
151C2×D3—64no—
152C2×D3—64no—
153C3×C4—24no—
154C3×C4—28no—
155C3×C4—48no—
156Dic3—64no—
157Dic3—68no—
158Dic3—128no—
159C32#195611yescharacteristic, complemented, Sylow
160C23—91no—
161Q8—24no—
162Q8—184no—
163Q8—364no—
164C2×C4—22no—
165C2×C4—92no—
166C2×C4—91no—
167C2×C4—92no—
168C2×C4—92no—
169C2×C4—94no—
170C2×C4—94no—
171C2×C4—182no—
172C2×C4—362no—
173C2×C4—362no—
174C2×C4—362no—
175C2×C4—364no—
176C2×C4C22⋊#15712yes—
177C2×C4C22×#15711yescharacteristic
178C8—184no—
179C2×C3—22no—
180C2×C3—24no—
181D3—64no—
182D3—62no—
183D3—62no—
184C22—91no—
185C22—91no—
186C22—92no—
187C22—92no—
188C22C2×C22⋊#15711yescharacteristic
189C4—42no—
190C4—92no—
191C4—94no—
192C4—362no—
193C4—722no—
194C4#6378414yescomplemented
195C4D4×#15712yes—
196C3—22no—
197C2—91no—
198C2—91no—
199C2—92no—
200C2#1059382711yescharacteristic
201C2C2×#6378412yes—
subgroupG/H
centerC22C2×C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×C4⋊Q8C4
socleC22×C32C2×C22⋊C4
prime radicalC22×C3⋊D3C2×D4
cosocleC2×C4×C3⋊D3C23
hypercenterC4⋊Q8#157
hypocenterC32#1956
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
9. C32×C4⋊Q8C4semidirect
10. #64153C4semidirect
14. #64078C4semidirect
90. C32×C4#103semidirect
93. C3⋊Dic3#103semidirect
100. C4⋊Q8#157semidirect
159. C32#1956semidirect
194. C4#63784semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×C4⋊Q82
C2×#637842
#105937352
C4×#37872
#19569