Finite Group Databasebeta

← #11795239

Subgroups — #11795239

Order 1152.

358 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 61 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#10593412C212yesmaximal
2#10590687C211yesmaximal, characteristic
3#10590658C211yesmaximal, characteristic
4#10590182C211yesmaximal, characteristic
5#10590049C212yesmaximal
6C2×C4⋊#157C2212yes—
7C2×#3773—22no—
8C2×C8×C3⋊D3C2211yescharacteristic
9#63900C2212yes—
10C4×#624C2211yescharacteristic
11C2×#3710C2211yescharacteristic
12#63737—22no—
13C3×#818—21no—
14C3×Dic3⋊C8—21no—
15#63576—21no—
16Dic3⋊(C3⋊C8)—21no—
17D3×#107—61no—
18D3×C4⋊C8—61no—
19C22×#157—22no—
20C2×C4×C3⋊D3C2311yescharacteristic
21C2×#624—22no—
22C2×#624D411yescharacteristic
23C2×#624D411yescharacteristic
24C4⋊#157—22no—
25C4⋊#157Q814yes—
26#3773—44no—
27C2×C32×C8D411yescharacteristic
28C2×C3⋊(C3⋊C8)D411yescharacteristic
29C8×C3⋊D3—22no—
30C3×C4⋊Dic3—22no—
31C3×C4×Dic3—21no—
32C2×C3×C3⋊C8—21no—
33#3724—22no—
34Dic32—21no—
35#3710—22no—
36#2087—91nomaximal, Sylow
37C2×D3×C8—61no—
38C2×D3×C8—61no—
39C2×D3×C8—61no—
40D3×C4⋊C4—62no—
41C42×D3—61no—
42C3×#107—61no—
43C3×C4⋊C8—61no—
44#818—21no—
45Dic3⋊C8—21no—
46Dic3⋊C8—61no—
47#807—62no—
48C4⋊(C3⋊C8)—61no—
49C22×C3⋊D3C2×D411yescharacteristic
50C2×#157—24no—
51C2×#157—42no—
52C2×#157—42no—
53C2×C32×C4C2×D411yescharacteristic
54C2×C3⋊Dic3#4111yescharacteristic
55C4×C3⋊D3C2×Q812yes—
56C4×C3⋊D3#4112yes—
57C2×C3×Dic3—21no—
58C2×C3×Dic3—21no—
59C2×C3×Dic3—42no—
60#624—21no—
61#624—22no—
62#624—42no—
63#624—42no—
64#624Q1612yes—
65C32×C8—21no—
66C3⋊(C3⋊C8)—21no—
67C3×C3⋊C8—41no—
68C2×#107—91no—
69C2×C4⋊C8—91no—
70#389—92no—
71#340—92no—
72#340—91no—
73C2×C4×D3—61no—
74C2×C4×D3—61no—
75C2×C4×D3—61no—
76C2×C4×D3—61no—
77C2×C4×D3—122no—
78C2×C3×C8—21no—
79C2×C3×C8—21no—
80C2×C3×C8—61no—
81C3×C4⋊C4—62no—
82C3×C42—61no—
83C4⋊Dic3—22no—
84Dic3⋊C4—122no—
85C4×Dic3—21no—
86C4×Dic3—61no—
87C4×Dic3—61no—
88C2×C3⋊C8—21no—
89C2×C3⋊C8—61no—
90C2×C3⋊C8—61no—
91D3×C8—64no—
92D3×C8—122no—
93D3×C8—122no—
94C22×C32#12111yescharacteristic
95C2×C3⋊D3C22⋊Q812yes—
96C2×C3⋊D3C2×Q1611yescharacteristic
97C2×C3⋊D3#13511yescharacteristic
98C2×C3⋊D3AGL(1,ℤ/8)12yes—
99#157—44no—
100C32×C4#12311yescharacteristic
101C32×C4C4⋊Q811yescharacteristic
102C3⋊Dic3#12512yes—
103C3×Dic3—22no—
104C3×Dic3—41no—
105C3×Dic3—82no—
106C22×C8—91no—
107C22×C8—91no—
108C2×C4⋊C4—92no—
109C2×C4⋊C4—92no—
110C2×C4⋊C4—182no—
111C2×C42—91no—
112#107—61no—
113#107—181no—
114C4⋊C8—61no—
115C4⋊C8—181no—
116#95—182no—
117C22×D3—61no—
118C22×D3—61no—
119C2×C3×C4—21no—
120C2×C3×C4—21no—
121C2×C3×C4—61no—
122C2×C3×C4—61no—
123C2×C3×C4—122no—
124C2×Dic3—21no—
125C2×Dic3—21no—
126C2×Dic3—42no—
127C2×Dic3—61no—
128C2×Dic3—61no—
129C4×D3—62no—
130C4×D3—62no—
131C4×D3—62no—
132C4×D3—62no—
133C4×D3—62no—
134C4×D3—62no—
135C4×D3—122no—
136C4×D3—242no—
137C4×D3—242no—
138C3×C8—22no—
139C3×C8—41no—
140C3×C8—121no—
141C3⋊C8—41no—
142C3⋊C8—62no—
143C3⋊C8—121no—
144C2×C32#39811yescharacteristic
145C2×C32#46711yescharacteristic
146C2×C32#46911yescharacteristic
147C3⋊D3#47712yes—
148C3⋊D3#47812yes—
149C22×C4—91no—
150C22×C4—91no—
151C22×C4—91no—
152C22×C4—182no—
153C22×C4—182no—
154C2×C8—61no—
155C2×C8—91no—
156C2×C8—182no—
157C2×C8—182no—
158C2×C8GO+(4,𝔽2)11yescharacteristic
159C4⋊C4—62no—
160C4⋊C4—94no—
161C4⋊C4—182no—
162C4⋊C4—182no—
163C4⋊C4—364no—
164C42—61no—
165C42—181no—
166C22×C3—21no—
167C22×C3—21no—
168C2×D3—62no—
169C2×D3—62no—
170C2×D3—61no—
171C2×D3—61no—
172C2×D3—62no—
173C2×D3—62no—
174C2×D3—61no—
175C2×D3—61no—
176C3×C4—21no—
177C3×C4—21no—
178C3×C4—21no—
179C3×C4—21no—
180C3×C4—62no—
181C3×C4—121no—
182C3×C4—242no—
183Dic3—22no—
184Dic3—41no—
185Dic3—62no—
186Dic3—62no—
187Dic3—82no—
188C32#208711yescharacteristic, complemented, Sylow
189C23—91no—
190C2×C4—61no—
191C2×C4—61no—
192C2×C4—92no—
193C2×C4—91no—
194C2×C4—92no—
195C2×C4—92no—
196C2×C4—122no—
197C2×C4—181no—
198C2×C4—182no—
199C2×C4—184no—
200C2×C4—362no—
201C2×C4—362no—
202C2×C4—362no—
203C2×C4—362no—
204C2×C4C2×GO+(4,𝔽2)11yescharacteristic
205C8—21no—
206C8—121no—
207C8—181no—
208C2×C3—21no—
209C2×C3—21no—
210C2×C3—21no—
211C2×C3—21no—
212C2×C3—21no—
213C2×C3—21no—
214D3—62no—
215D3—62no—
216D3—62no—
217D3—62no—
218C22—92no—
219C22—91no—
220C22—91no—
221C22—92no—
222C22#6423011yescharacteristic
223C4—62no—
224C4—92no—
225C4—121no—
226C4—242no—
227C4—364no—
228C4#6422211yescharacteristic
229C4#6423311yescharacteristic
230C3—21no—
231C3—21no—
232C2—92no—
233C2—92no—
234C2#1059328711yescharacteristic
235C2#1059328811yescharacteristic
236C2#1059333911yescharacteristic
subgroupG/H
centerC22#64230
commutator, cosocleC2×C4×C3⋊D3C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC22×C32#121
prime radicalC22×C3⋊D3C2×D4
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#2087
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
188. C32#2087semidirect

Maximal subgroups

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

subgroupindex
#105934122
#105906872
#105906582
#105901822
#105900492
#20879