Finite Group Databasebeta

← #11799793

Subgroups — #11799793

Order 1152.

282 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 41 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#10590839C211yesmaximal, characteristic
2#10590687C211yesmaximal, characteristic, complemented
3#10590176C211yesmaximal, characteristic, complemented
4#10590068C212yesmaximal, complemented
5#10590061C212yesmaximal, complemented
6C2×C8×C3⋊D3C2211yescharacteristic
7#63916—21no—
8#63900—21no—
9C2×#3713C2211yescharacteristic
10C2×#3708C2212yes—
11C3×#821—21no—
12C3×#818—21no—
13#63576C2212yes—
14#63576C2211yescharacteristic
15D3×#107—61no—
16#4775—61no—
17C2×C4×C3⋊D3D411yescharacteristic
18C2×C3×D12—21no—
19C2×#626—41no—
20C2×#624—41no—
21C2×C32×C8D411yescharacteristic
22C2×C3⋊(C3⋊C8)C2311yescharacteristic
23C8×C3⋊D3—22no—
24C3×C4⋊Dic3—22no—
25C3×C4⋊Dic3—21no—
26#3724—41no—
27(C2×D3)⋊Dic3—41no—
28#3713—22no—
29#3708—22no—
30#2232—91nomaximal, Sylow
31#938—61no—
32C2×#213—61no—
33C2×D3×C8—61no—
34C2×D3×C8—61no—
35#895—61no—
36D3×C4⋊C4—62no—
37C3×#107—61no—
38C3×#102—61no—
39#821—21no—
40#818—21no—
41#807—62no—
42#807—61no—
43C22×C3⋊D3D811yescharacteristic
44C22×C3×D3—41no—
45C2×C32×C4C2×D411yescharacteristic
46C2×C3⋊Dic3D811yescharacteristic
47C4×C3⋊D3—21no—
48C4×C3⋊D3—21no—
49C2×C3×Dic3—41no—
50C2×C3×Dic3—42no—
51C3×D12—41no—
52C3×D12—41no—
53#626—82no—
54#624—82no—
55C32×C8—21no—
56C3⋊(C3⋊C8)#4112yes—
57#466—91no—
58C2×#107—91no—
59#366—92no—
60#357—92no—
61C22⋊C16—91no—
62C2×C3×D4—61no—
63C2×#67—121no—
64C2×D12—21no—
65C2×D12—121no—
66C2×C4×D3—61no—
67C2×C4×D3—61no—
68C2×C4×D3—122no—
69C2×C3×C8—21no—
70C2×C3×C8—21no—
71C3×C4⋊C4—61no—
72C3×C4⋊C4—62no—
73#217—121no—
74#213—122no—
75(C2×D3)⋊C4—121no—
76C4⋊Dic3—22no—
77C4⋊Dic3—21no—
78Dic3⋊C4—122no—
79C2×C3⋊C8—61no—
80C2×C3⋊C8—61no—
81D3×C8—64no—
82D3×C8—122no—
83C22×C32C2×D811yescharacteristic
84C2×C3⋊D3—21no—
85C2×C3⋊D3—21no—
86C2×C3⋊D3D1612yes—
87C2×C3×D3—81no—
88C2×C3×D3—81no—
89C2×C3×D3—81no—
90C32×C4#12311yescharacteristic
91C32×C4#13711yescharacteristic
92C3⋊Dic3—21no—
93C3×Dic3—82no—
94C3×Dic3—81no—
95C2×D8—91no—
96C22×C8—91no—
97#121—181no—
98C2×C4⋊C4—181no—
99C2×C16—92no—
100#107—61no—
101#107—92no—
102#107—91no—
103#102—61no—
104C23×C3—121no—
105C22×D3—41no—
106C22×D3—61no—
107C22×D3—61no—
108C3×D4—121no—
109C3×D4—121no—
110C2×C3×C4—21no—
111C2×C3×C4—21no—
112C2×C3×C4—122no—
113C2×C3×C4—121no—
114#67—242no—
115C2×Dic3—42no—
116C2×Dic3—41no—
117C2×Dic3—61no—
118C2×Dic3—61no—
119D12—41no—
120D12—41no—
121D12—242no—
122C4×D3—62no—
123C4×D3—62no—
124C4×D3—121no—
125C4×D3—121no—
126C4×D3—244no—
127C3×C8—22no—
128C3×C8—41no—
129C3⋊C8—62no—
130C3⋊C8—62no—
131C2×C32#48011yescharacteristic
132C2×C32C2×D1611yescharacteristic
133C2×C32#51011yescharacteristic
134C3⋊D3—22no—
135C3×D3—161no—
136C2×D4—61no—
137C2×D4—361no—
138C22×C4—91no—
139C22×C4—361no—
140D8—182no—
141C2×C8—91no—
142C2×C8—182no—
143C2×C8GO+(4,𝔽2)11yescharacteristic
144C4⋊C4—61no—
145C4⋊C4—62no—
146C4⋊C4—361no—
147C22⋊C4—361no—
148C16—182no—
149C22×C3—21no—
150C22×C3—21no—
151C22×C3—241no—
152C22×C3—241no—
153C22×C3—241no—
154C2×D3—62no—
155C2×D3—62no—
156C2×D3—62no—
157C2×D3—62no—
158C2×D3—81no—
159C2×D3—81no—
160C2×D3—81no—
161C2×D3—121no—
162C2×D3—121no—
163C3×C4—21no—
164C3×C4—21no—
165C3×C4—21no—
166C3×C4—21no—
167C3×C4—242no—
168C3×C4—241no—
169Dic3—62no—
170Dic3—82no—
171Dic3—81no—
172Dic3—121no—
173C32#223211yescharacteristic, complemented, Sylow
174C23—91no—
175C23—121no—
176D4—121no—
177D4—121no—
178D4—722no—
179C2×C4—91no—
180C2×C4—121no—
181C2×C4—122no—
182C2×C4—181no—
183C2×C4—181no—
184C2×C4—722no—
185C2×C4C2×GO+(4,𝔽2)11yescharacteristic
186C8—21no—
187C8—92no—
188C2×C3—21no—
189C2×C3—21no—
190C2×C3—21no—
191C2×C3—21no—
192C2×C3—21no—
193C2×C3—21no—
194C2×C3—481no—
195D3—64no—
196D3—122no—
197D3—161no—
198C22—92no—
199C22—181no—
200C22—181no—
201C22—241no—
202C22—241no—
203C22—241no—
204C22#6422511yescharacteristic
205C4—181no—
206C4—242no—
207C4—241no—
208C4#6422611yescharacteristic
209C4#6423311yescharacteristic
210C3—21no—
211C3—21no—
212C2—182no—
213C2—481no—
214C2#1059327611yescharacteristic
215C2#1059327911yescharacteristic
216C2#1059336811yescharacteristic
subgroupG/H
centerC22#64225
commutator, cosocleC2×C3⋊(C3⋊C8)C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC22×C32C2×D8
prime radical#10590839C2
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#2232
LCSG ▷ C2×C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. #10590687C2semidirect
3. #10590176C2semidirect
4. #10590068C2semidirect
5. #10590061C2semidirect
173. C32#2232semidirect

Maximal subgroups

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

subgroupindex
#105908392
#105906872
#105901762
#105900682
#105900612
#22329