Finite Group Databasebeta

← #11795320

Subgroups — #11795320

Order 1152.

298 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 51 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#10593394C212yesmaximal
2#10590701C211yesmaximal, characteristic
3#10590687C211yesmaximal, characteristic
4#10590185C211yesmaximal, characteristic
5#10590052C212yesmaximal
6C2×#3788C2212yes—
7C2×C8×C3⋊D3C2211yescharacteristic
8#63900C2212yes—
9#63874C2211yescharacteristic
10C2×#3712C2211yescharacteristic
11#63743—22no—
12#63742—22no—
13C3×#818—21no—
14C3×Dic3⋊C8—21no—
15#63576—21no—
16Dic3⋊(C3⋊C8)—21no—
17D3×#107—61no—
18#4839—61no—
19C2×C4×C3⋊D3C2311yescharacteristic
20C2×#624—22no—
21C2×#622—22no—
22#3788—22no—
23#3788Q814yes—
24C2×C32×C8D411yescharacteristic
25C2×C3⋊(C3⋊C8)D411yescharacteristic
26C8×C3⋊D3—22no—
27C3×C4⋊Dic3—22no—
28C3×C4×Dic3—21no—
29C2×C3×C3⋊C8—21no—
30#3724—22no—
31#3724D411yescharacteristic
32#3724D411yescharacteristic
33#3722—21no—
34#3712—22no—
35#2089—91nomaximal, Sylow
36C2×ΓL(1,𝔽25)—61no—
37C2×D3×C8—61no—
38C2×D3×C8—61no—
39D3×C4⋊C4—62no—
40#872—61no—
41C3×#107—61no—
42C3×C4⋊C8—61no—
43#818—21no—
44Dic3⋊C8—21no—
45Dic3⋊C8—61no—
46#807—62no—
47C4⋊(C3⋊C8)—61no—
48C22×C3⋊D3#4111yescharacteristic
49C2×C32×C4C2×D411yescharacteristic
50C2×C3⋊Dic3C2×D411yescharacteristic
51C4×C3⋊D3C2×Q812yes—
52C4×C3⋊D3#4112yes—
53C2×C3×Dic3—21no—
54C2×C3×Dic3—21no—
55C2×C3×Dic3—42no—
56#624—82no—
57#622—24no—
58C32×C8—21no—
59C3⋊(C3⋊C8)—21no—
60C3×C3⋊C8—41no—
61#428—92no—
62C2×#107—91no—
63#424—91no—
64#343—92no—
65#341—91no—
66C2×C4×D3—61no—
67C2×C4×D3—61no—
68C2×C4×D3—122no—
69C2×C3×C8—21no—
70C2×C3×C8—21no—
71C2×C3×C8—61no—
72C3×C4⋊C4—62no—
73C3×C42—61no—
74(C2×D3)⋊C4—61no—
75(C2×D3)⋊C4—61no—
76C4⋊Dic3—22no—
77Dic3⋊C4—61no—
78Dic3⋊C4—61no—
79Dic3⋊C4—122no—
80C4×Dic3—21no—
81C2×C3⋊C8—21no—
82C2×C3⋊C8—61no—
83C2×C3⋊C8—61no—
84ΓL(1,𝔽25)—122no—
85D3×C8—64no—
86D3×C8—122no—
87C22×C32#12111yescharacteristic
88C2×C3⋊D3—21no—
89C2×C3⋊D3—21no—
90C2×C3⋊D3#12512yes—
91C32×C4#12311yescharacteristic
92C32×C4C4⋊Q811yescharacteristic
93C3⋊Dic3C22⋊Q812yes—
94C3×Dic3—41no—
95C3×Dic3—41no—
96C3×Dic3—82no—
97C2×M16—91no—
98C2×M16—92no—
99C22×C8—91no—
100#117—91no—
101C2×C4⋊C4—92no—
102#107—61no—
103#107—181no—
104#107—182no—
105#106—182no—
106C4⋊C8—61no—
107C4⋊C8—181no—
108C22×D3—61no—
109C22×D3—61no—
110C2×C3×C4—21no—
111C2×C3×C4—21no—
112C2×C3×C4—61no—
113C2×C3×C4—61no—
114C2×C3×C4—122no—
115C2×Dic3—21no—
116C2×Dic3—21no—
117C2×Dic3—42no—
118C2×Dic3—61no—
119C2×Dic3—61no—
120C4×D3—62no—
121C4×D3—62no—
122C4×D3—62no—
123C4×D3—62no—
124C4×D3—244no—
125C3×C8—22no—
126C3×C8—41no—
127C3×C8—121no—
128C3⋊C8—41no—
129C3⋊C8—62no—
130C3⋊C8—121no—
131C2×C32#39811yescharacteristic
132C2×C32#47211yescharacteristic
133C2×C32#47311yescharacteristic
134C3⋊D3—22no—
135C22×C4—91no—
136C22×C4—182no—
137M16—94no—
138M16—182no—
139M16—182no—
140C2×C8—61no—
141C2×C8—91no—
142C2×C8—182no—
143C2×C8—182no—
144C2×C8GO+(4,𝔽2)11yescharacteristic
145C4⋊C4—62no—
146C4⋊C4—91no—
147C4⋊C4—91no—
148C4⋊C4—182no—
149C22⋊C4—181no—
150C42—61no—
151C22×C3—21no—
152C22×C3—21no—
153C2×D3—62no—
154C2×D3—62no—
155C2×D3—62no—
156C2×D3—62no—
157C2×D3—121no—
158C2×D3—121no—
159C3×C4—21no—
160C3×C4—21no—
161C3×C4—21no—
162C3×C4—21no—
163C3×C4—121no—
164C3×C4—121no—
165C3×C4—242no—
166Dic3—41no—
167Dic3—41no—
168Dic3—62no—
169Dic3—62no—
170Dic3—82no—
171C32#208911yescharacteristic, complemented, Sylow
172C23—91no—
173C2×C4—61no—
174C2×C4—61no—
175C2×C4—91no—
176C2×C4—92no—
177C2×C4—92no—
178C2×C4—122no—
179C2×C4—722no—
180C2×C4C2×GO+(4,𝔽2)11yescharacteristic
181C8—21no—
182C8—121no—
183C8—184no—
184C8—181no—
185C2×C3—21no—
186C2×C3—21no—
187C2×C3—21no—
188C2×C3—21no—
189C2×C3—21no—
190C2×C3—21no—
191D3—64no—
192D3—122no—
193C22—92no—
194C22—181no—
195C22—181no—
196C22#6423011yescharacteristic
197C4—92no—
198C4—121no—
199C4—121no—
200C4—242no—
201C4#6422211yescharacteristic
202C4#6423311yescharacteristic
203C3—21no—
204C3—21no—
205C2—182no—
206C2#1059330311yescharacteristic
207C2#1059330411yescharacteristic
208C2#1059333911yescharacteristic
subgroupG/H
centerC22#64230
commutator, cosocleC2×C4×C3⋊D3C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC22×C32#121
prime radicalC22×C3⋊D3#41
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#2089
LCSG ▷ C2×C4×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
171. C32#2089semidirect

Maximal subgroups

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

subgroupindex
#105933942
#105907012
#105906872
#105901852
#105900522
#20899