Finite Group Databasebeta

← #11797109

Subgroups — #11797109

Order 1152.

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

normal subgroups only

This group has 270 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#10593762C211yesmaximal, characteristic
2#10590913C211yesmaximal, characteristic
3#10590685C211yesmaximal, characteristic
4#10590067C214yesmaximal, complemented
5C2×C8×C3⋊D3C2211yescharacteristic
6#63900—21no—
7#63818—21no—
8#63773C2212yes—
9#63765C412yescomplemented
10#63764C412yescomplemented
11C3×#819—21no—
12C3×#817—21no—
13#63578C2212yes—
14#63574C2212yes—
15D3×#108—61no—
16D3×#106—61no—
17C2×C4×C3⋊D3D411yescharacteristic
18C2×#624—41no—
19C2×C32×C8D411yescharacteristic
20C2×C3⋊(C3⋊C8)C2311yescharacteristic
21C8×C3⋊D3C2×C411yescharacteristic
22C8×C3⋊D3C2×C411yescharacteristic
23C8×C3⋊D3Q811yescharacteristic
24C8×C3⋊D3Q811yescharacteristic
25C3×C4⋊Dic3—22no—
26C3×#208—22no—
27#3724—41no—
28#3712—41no—
29#3710—41no—
30#3708C2×C414yescomplemented
31C2×#365—91nomaximal, Sylow
32D3×M16—62no—
33C2×D3×C8—61no—
34C2×D3×C8—61no—
35D3×C4⋊C4—62no—
36C3×#108—61no—
37C3×#106—61no—
38#822—62no—
39#819—21no—
40#817—21no—
41#808—62no—
42C22×C3⋊D3SD1611yescharacteristic
43C2×C32×C4C2×D411yescharacteristic
44C2×C3⋊Dic3SD1611yescharacteristic
45C4×C3⋊D3C4⋊C411yescharacteristic
46C4×C3⋊D3C4⋊C411yescharacteristic
47C4×C3⋊D3SD1611yescharacteristic
48C4×C3⋊D3SD1611yescharacteristic
49C2×C3×Dic3—42no—
50#624—82no—
51C32×C8C4⋊C411yescharacteristic
52C32×C8C4⋊C411yescharacteristic
53C3⋊(C3⋊C8)C22×C411yescharacteristic
54C3⋊(C3⋊C8)C2×Q811yescharacteristic
55C3×C3⋊C8—42no—
56C2×M32—91no—
57C2×#108—91no—
58C2×#106—91no—
59#365—94no—
60C2×C4×D3—61no—
61C2×C4×D3—61no—
62C2×C4×D3—122no—
63C3×M16—62no—
64C2×C3×C8—21no—
65C2×C3×C8—21no—
66C3×C4⋊C4—62no—
67C4⋊Dic3—22no—
68Dic3⋊C4—122no—
69#208—22no—
70C2×C3⋊C8—61no—
71C2×C3⋊C8—61no—
72ΓL(1,𝔽25)—122no—
73D3×C8—61no—
74D3×C8—61no—
75D3×C8—61no—
76D3×C8—61no—
77D3×C8—61no—
78D3×C8—61no—
79D3×C8—61no—
80D3×C8—61no—
81D3×C8—122no—
82C22×C32C2×SD1611yescharacteristic
83C2×C3⋊D3—22no—
84C2×C3⋊D3#10611yescharacteristic
85C2×C3⋊D3#10611yescharacteristic
86C32×C4C2×C4⋊C411yescharacteristic
87C32×C4C2×SD1611yescharacteristic
88C3⋊Dic3#10611yescharacteristic
89C3⋊Dic3#10611yescharacteristic
90C3×Dic3—82no—
91C2×M16—181no—
92C22×C8—91no—
93C2×C4⋊C4—181no—
94M32—92no—
95M32—92no—
96C2×C16—92no—
97#108—61no—
98#108—92no—
99#106—61no—
100#106—92no—
101C22×D3—61no—
102C22×D3—61no—
103C2×C3×C4—21no—
104C2×C3×C4—21no—
105C2×C3×C4—122no—
106C2×Dic3—42no—
107C2×Dic3—61no—
108C2×Dic3—61no—
109C4×D3—61no—
110C4×D3—61no—
111C4×D3—61no—
112C4×D3—61no—
113C4×D3—61no—
114C4×D3—61no—
115C4×D3—61no—
116C4×D3—61no—
117C4×D3—244no—
118C3×C8—21no—
119C3×C8—21no—
120C3×C8—21no—
121C3×C8—21no—
122C3×C8—122no—
123C3⋊C8—42no—
124C3⋊C8—61no—
125C3⋊C8—61no—
126C3⋊C8—61no—
127C3⋊C8—61no—
128C2×C32—21no—
129C2×C32C2×#10611yescharacteristic
130C3⋊D3—21no—
131C3⋊D3#36512yescomplemented
132C22×C4—91no—
133C22×C4—361no—
134M16—62no—
135M16—361no—
136C2×C8—91no—
137C2×C8—91no—
138C2×C8—91no—
139C2×C8—91no—
140C2×C8—91no—
141C2×C8—361no—
142C2×C8GO+(4,𝔽2)11yescharacteristic
143C4⋊C4—62no—
144C4⋊C4—361no—
145C16—94no—
146C22×C3—21no—
147C22×C3—21no—
148C2×D3—61no—
149C2×D3—61no—
150C2×D3—61no—
151C2×D3—61no—
152C2×D3—64no—
153C2×D3—122no—
154C3×C4—21no—
155C3×C4—21no—
156C3×C4—21no—
157C3×C4—21no—
158C3×C4—242no—
159Dic3—61no—
160Dic3—61no—
161Dic3—61no—
162Dic3—61no—
163Dic3—82no—
164C32C2×#36511yescharacteristic, complemented, Sylow
165C23—91no—
166C2×C4—91no—
167C2×C4—91no—
168C2×C4—91no—
169C2×C4—91no—
170C2×C4—91no—
171C2×C4—122no—
172C2×C4—722no—
173C2×C4C2×GO+(4,𝔽2)11yescharacteristic
174C8—91no—
175C8—91no—
176C8—122no—
177C8#377311yescharacteristic
178C8#377311yescharacteristic
179C2×C3—22no—
180C2×C3—21no—
181C2×C3—21no—
182C2×C3—41no—
183D3—62no—
184D3—62no—
185D3—62no—
186D3—121no—
187C22—91no—
188C22—91no—
189C22—182no—
190C22#6422711yescharacteristic
191C4—91no—
192C4—91no—
193C4—242no—
194C4#6422711yescharacteristic
195C4C2×#377311yescharacteristic
196C3—21no—
197C3—21no—
198C2—21no—
199C2—92no—
200C2—181no—
201C2#1059338711yescharacteristic
subgroupG/H
centerC2#10593387
commutatorC3⋊(C3⋊C8)C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC2×C32C2×#106
prime radicalC22×C3⋊D3SD16
cosocleC2×C3⋊(C3⋊C8)C23
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32C2×#365
LCSG ▷ C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
4. #10590067C2semidirect
9. #63765C4semidirect
10. #63764C4semidirect
30. #3708C2×C4semidirect
131. C3⋊D3#365semidirect
164. C32C2×#365semidirect

Maximal subgroups

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

subgroupindex
#105937622
#105909132
#105906852
#105900672
C2×#3659