Finite Group Databasebeta

← #11781765

Subgroups — #11781765

Order 1152.

498 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 119 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#10592791C211yesmaximal, characteristic, complemented
2#10592786C211yesmaximal, characteristic
3#10592545C211yesmaximal, characteristic
4#10592537C211yesmaximal, characteristic
5C32×#332C211yesmaximal, characteristic, complemented
6#10589348C211yesmaximal, characteristic, complemented
7#10589346C211yesmaximal, characteristic, complemented
8#68449—34nomaximal
9C32×C4⋊Q8C2211yescharacteristic
10C2×#3756—21no—
11C2×#3756—21no—
12C2×#3743—21no—
13C4×C4⋊(C3⋊D3)C2211yescharacteristic
14#64078C2211yescharacteristic
15C32×C4⋊C8C2211yescharacteristic
16C32×C4⋊C8C2211yescharacteristic
17#63648—21no—
18#63647—21no—
19#63645—21no—
20#63636—21no—
21#63634—21no—
22C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
23C4×C3⋊(C3⋊C8)C2211yescharacteristic
24#5092—34no—
25#5087—34no—
26#4846—34no—
27#4838—34no—
28C3×#332D314yescomplemented
29#4482—34no—
30#4480—34no—
31C2×C32×Q8—21no—
32C2×C4⋊(C3⋊D3)D411yescharacteristic
33C2×C4×C3⋊D3—21no—
34C2×#634—21no—
35C2×C32×C8—21no—
36C2×C32×C8—21no—
37C32×C4⋊C4—21no—
38C32×C4⋊C4—21no—
39C32×C42C2311yescharacteristic
40#3756—42no—
41#3756—42no—
42#3752—21no—
43C4⋊(C3⋊Dic3)—21no—
44C4⋊(C3⋊Dic3)—21no—
45C4⋊(C3⋊Dic3)D411yescharacteristic
46C2×C3⋊(C3⋊C8)—21no—
47C2×C3⋊(C3⋊C8)D411yescharacteristic
48C2×C3⋊(C3⋊C8)D411yescharacteristic
49#3743—42no—
50#1689—91noSylow
51C3×C4⋊Q8C2×D314yes—
52C2×#216—64no—
53C2×#216—64no—
54C2×ΓL(1,𝔽25)—64no—
55C4×D12—34no—
56#869—34no—
57C3×C4⋊C8C2×D314yes—
58C3×C4⋊C8C2×D314yes—
59#821—64no—
60(C2×D3)⋊C8—64no—
61#818—64no—
62#809—64no—
63#807—64no—
64C4⋊(C3⋊C8)—34no—
65C4×C3⋊C8—34no—
66C22×C3⋊D3—21no—
67C32×Q8—41no—
68C32×Q8—41no—
69C2×C32×C4—41no—
70C2×C32×C4C2×D411yescharacteristic
71C2×C32×C4C2×D411yescharacteristic
72C2×C32×C4#4111yescharacteristic
73C2×C3⋊Dic3—21no—
74C2×C3⋊Dic3—41no—
75C4⋊(C3⋊D3)—21no—
76C4⋊(C3⋊D3)—21no—
77C4×C3⋊D3—41no—
78C4×C3⋊D3—41no—
79#634—41no—
80#634—41no—
81C32×C8—41no—
82C32×C8—41no—
83C3⋊(C3⋊C8)—21no—
84C3⋊(C3⋊C8)—41no—
85C3⋊(C3⋊C8)D812yes—
86#494—91no—
87#474—91no—
88#474—91no—
89#436—91no—
90#334—91no—
91#332—91no—
92#332C3⋊D311yescharacteristic, complemented
93C2×C3×Q8—24no—
94C2×D12—34no—
95C2×C4×D3—64no—
96C2×Dic6—64no—
97C2×C3×C8—24no—
98C2×C3×C8—24no—
99C3×C4⋊C4—24no—
100C3×C4⋊C4—24no—
101C3×C42C22×D314yes—
102#216—128no—
103#216—128no—
104(C2×D3)⋊C4—64no—
105C4⋊Dic3—34no—
106C4⋊Dic3—64no—
107C4⋊Dic3—64no—
108C2×C3⋊C8—34no—
109C2×C3⋊C8—34no—
110C2×C3⋊C8—64no—
111ΓL(1,𝔽25)—128no—
112C22×C32#12111yescharacteristic
113C2×C3⋊D3—41no—
114C2×C3⋊D3—41no—
115C2×C3⋊D3—41no—
116C32×C4—21no—
117C32×C4—81no—
118C32×C4C2×D811yescharacteristic
119C32×C4AGL(1,ℤ/8)11yescharacteristic
120C32×C4#13711yescharacteristic
121C32×C4#13711yescharacteristic
122C3⋊Dic3—41no—
123C3⋊Dic3—81no—
124C2×Q16—181no—
125C2×Q16—181no—
126C2×M16—181no—
127C4⋊Q8—91no—
128C4⋊Q8C2×C3⋊D311yescharacteristic
129C4×D4—91no—
130#107—181no—
131#107—181no—
132C4⋊C8—91no—
133C4⋊C8C2×C3⋊D311yescharacteristic
134C4⋊C8C2×C3⋊D311yescharacteristic
135#102—181no—
136#102—181no—
137C22⋊C8—181no—
138C4×C8—91no—
139C22×D3—64no—
140C3×Q8—44no—
141C3×Q8—44no—
142C2×C3×C4—44no—
143C2×C3×C4#23514yes—
144C2×C3×C4D3×D414yes—
145C2×C3×C4D3×D414yes—
146C2×Dic3—64no—
147C2×Dic3—124no—
148D12—64no—
149D12—64no—
150C4×D3—124no—
151C4×D3—124no—
152Dic6—124no—
153Dic6—124no—
154C3×C8—44no—
155C3×C8—44no—
156C3⋊C8—38no—
157C3⋊C8—64no—
158C3⋊C8—124no—
159C2×C32#45911yescharacteristic
160C2×C32#47011yescharacteristic
161C2×C32#47311yescharacteristic
162C3⋊D3—81no—
163C2×Q8—21no—
164C2×Q8—181no—
165C2×D4—91no—
166C22×C4—181no—
167Q16—362no—
168Q16—362no—
169M16—362no—
170C2×C8—21no—
171C2×C8—21no—
172C2×C8—91no—
173C2×C8—91no—
174C2×C8—181no—
175C4⋊C4—21no—
176C4⋊C4—21no—
177C4⋊C4—91no—
178C4⋊C4—181no—
179C4⋊C4—181no—
180C22⋊C4—181no—
181C42C22×C3⋊D311yescharacteristic
182C22×C3#88414yes—
183C2×D3—124no—
184C2×D3—124no—
185C2×D3—124no—
186C3×C4—24no—
187C3×C4—84no—
188C3×C4D3×D814yes—
189C3×C4#91414yes—
190C3×C4#91514yes—
191C3×C4#91814yes—
192Dic3—124no—
193Dic3—244no—
194C32#168911yescharacteristic, complemented, Sylow
195C23—181no—
196Q8—41no—
197Q8—41no—
198Q8—361no—
199Q8—361no—
200D4—181no—
201D4—181no—
202C2×C4—41no—
203C2×C4—181no—
204C2×C4—361no—
205C2×C4—361no—
206C2×C4—361no—
207C2×C4#382811yescharacteristic
208C2×C4D4×C3⋊D311yescharacteristic
209C2×C4D4×C3⋊D311yescharacteristic
210C8—41no—
211C8—41no—
212C8—92no—
213C8—181no—
214C8—361no—
215C2×C3#475514yes—
216C2×C3#478614yes—
217C2×C3#481614yes—
218D3—244no—
219C22—361no—
220C22—361no—
221C22—361no—
222C22#6409311yescharacteristic
223C4—21no—
224C4—81no—
225C4—361no—
226C4—721no—
227C4D8×C3⋊D311yescharacteristic
228C4#6412311yescharacteristic
229C4#6412411yescharacteristic
230C4#6412711yescharacteristic
231C3#6844914yescomplemented
232C2—721no—
233C2#1059245411yescharacteristic
234C2#1059248511yescharacteristic
235C2#1059251511yescharacteristic
subgroupG/H
centerC22#64093
commutator, cosocleC32×C42C23
FrattiniC42C22×C3⋊D3
FittingC32×#332C2
socleC22×C32#121
prime radicalC2×C4⋊(C3⋊D3)D4
hypercenter#332C3⋊D3
hypocenterC32#1689
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
1. #10592791C2semidirect
5. C32×#332C2semidirect
6. #10589348C2semidirect
7. #10589346C2semidirect
28. C3×#332D3semidirect
92. #332C3⋊D3semidirect
194. C32#1689semidirect
231. C3#68449semidirect

Maximal subgroups

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

subgroupindex
#105927912
#105927862
#105925452
#105925372
C32×#3322
#105893482
#105893462
#684493