Finite Group Databasebeta

← #11799725

Subgroups — #11799725

Order 1152.

228 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 37 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#10590389C211yesmaximal, characteristic
2#10590309C211yesmaximal, characteristic, complemented
3#10590150C211yesmaximal, characteristic, complemented
4#10590067C212yesmaximal, complemented
5#10590064C212yesmaximal
6C3×#869—21no—
7#63822C2211yescharacteristic
8#63815—21no—
9#63773C2212yes—
10C4×C3⋊(C3⋊C8)C2211yescharacteristic
11C3×#805—21no—
12#63578C2211yescharacteristic
13#63574—21no—
14#63574C2212yes—
15#5080—61no—
16#4824—61no—
17C3×#235—21no—
18C2×C3×Dic6—41no—
19C32×C42D411yescharacteristic
20C2×C3⋊(C3⋊C8)D411yescharacteristic
21C2×C3⋊(C3⋊C8)C2311yescharacteristic
22C3×C4⋊Dic3—22no—
23C3×C4⋊Dic3—41no—
24C3×#208—21no—
25#3718Q811yescharacteristic, complemented
26#3715—21no—
27#3713Q811yescharacteristic, complemented
28#3711—41no—
29D3×C3⋊C8—41no—
30#3708—22no—
31#2230—91nomaximal, Sylow
32C3×C4⋊Q8—61no—
33#950—61no—
34#948—61no—
35#907—61no—
36#869—21no—
37C3×#104—61no—
38#822—61no—
39#808—62no—
40#808—62no—
41#805—21no—
42C4×C3⋊C8—61no—
43C4×C3⋊C8—61no—
44C2×C32×C4—21no—
45C2×C32×C4C2×D411yescharacteristic
46C3×#67—41no—
47C2×C3×Dic3—42no—
48C3×D12—21no—
49C3×C4×D3—41no—
50C3×Dic6—21no—
51C3×Dic6—82no—
52C3⋊(C3⋊C8)SD1611yescharacteristic
53C3⋊(C3⋊C8)SD1611yescharacteristic
54C3⋊(C3⋊C8)C2×Q811yescharacteristic
55C3⋊(C3⋊C8)#4111yescharacteristic
56C3×C3⋊C8—41no—
57#498—91no—
58#443—91no—
59#365—92no—
60#364—91no—
61#360—92no—
62C3×#41—61no—
63C2×C3×Q8—121no—
64#235—21no—
65C2×Dic6—41no—
66C3×M16—61no—
67C3×C4⋊C4—62no—
68C3×C4⋊C4—121no—
69C3×C42—21no—
70C3×C42—21no—
71#216—61no—
72#215—61no—
73#214—61no—
74#213—61no—
75C4⋊Dic3—22no—
76C4⋊Dic3—41no—
77#208—21no—
78#208—121no—
79C2×C3⋊C8—61no—
80C2×C3⋊C8—61no—
81C2×C3⋊C8—61no—
82C2×C3⋊C8—61no—
83C2×C3⋊C8—121no—
84ΓL(1,𝔽25)—121no—
85D3×C8—121no—
86C22×C32AGL(1,ℤ/8)11yescharacteristic
87C2×C3×D3—41no—
88C32×C4—22no—
89C32×C4C22⋊Q811yescharacteristic
90C32×C4C2×SD1611yescharacteristic
91C3×Dic3—41no—
92C3×Dic3—82no—
93#135—91no—
94#131—181no—
95C4⋊Q8—61no—
96M32—92no—
97#108—91no—
98#106—92no—
99#106—181no—
100#104—61no—
101C4×C8—91no—
102C3×Q8—61no—
103C3×Q8—242no—
104C3×D4—61no—
105C3×D4—121no—
106C2×C3×C4—21no—
107C2×C3×C4—21no—
108C2×C3×C4—21no—
109C2×C3×C4—21no—
110C2×C3×C4—41no—
111C2×C3×C4—121no—
112C2×C3×C4—122no—
113#67—41no—
114C2×Dic3—42no—
115D12—21no—
116C4×D3—41no—
117Dic6—21no—
118Dic6—82no—
119C3×C8—121no—
120C3⋊C8—41no—
121C3⋊C8—61no—
122C3⋊C8—61no—
123C3⋊C8—61no—
124C3⋊C8—61no—
125C3⋊C8—61no—
126C3⋊C8—61no—
127C3⋊C8—61no—
128C3⋊C8—61no—
129C2×C32—21no—
130C2×C32#47611yescharacteristic
131C3×D3—81no—
132#41—61no—
133C2×Q8—121no—
134Q16—91no—
135SD16—181no—
136D8—91no—
137M16—61no—
138M16—361no—
139C2×C8—91no—
140C2×C8—91no—
141C2×C8—361no—
142C4⋊C4—62no—
143C4⋊C4—121no—
144C42GO+(4,𝔽2)11yescharacteristic
145C16—182no—
146C22×C3—21no—
147C22×C3—21no—
148C22×C3—121no—
149C2×D3—41no—
150C3×C4—22no—
151C3×C4—22no—
152C3×C4—21no—
153C3×C4—21no—
154C3×C4—21no—
155C3×C4—21no—
156C3×C4—42no—
157C3×C4—121no—
158C3×C4—242no—
159Dic3—41no—
160Dic3—82no—
161C32#223011yescharacteristic, complemented, Sylow
162Q8—61no—
163Q8—242no—
164D4—61no—
165D4—121no—
166C2×C4—21no—
167C2×C4—121no—
168C2×C4—122no—
169C2×C4C2×GO+(4,𝔽2)11yescharacteristic
170C8—91no—
171C8—91no—
172C8—91no—
173C8—91no—
174C8—121no—
175C2×C3—21no—
176C2×C3—21no—
177C2×C3—21no—
178C2×C3—21no—
179C2×C3—41no—
180C2×C3—241no—
181D3—81no—
182C22—121no—
183C22#6423611yescharacteristic
184C4—22no—
185C4—121no—
186C4—242no—
187C4D32⋊Q811yescharacteristic
188C4#6422711yescharacteristic
189C3—21no—
190C3—21no—
191C2—21no—
192C2—241no—
193C2#1059335711yescharacteristic
subgroupG/H
centerC2#10593357
commutator, cosocleC2×C3⋊(C3⋊C8)C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C42D4
socleC2×C32#476
prime radical#63822C22
hypercenterC42GO+(4,𝔽2)
hypocenterC32#2230
LCSG ▷ C2×C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
2. #10590309C2semidirect
3. #10590150C2semidirect
4. #10590067C2semidirect
25. #3718Q8semidirect
27. #3713Q8semidirect
161. C32#2230semidirect

Maximal subgroups

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

subgroupindex
#105903892
#105903092
#105901502
#105900672
#105900642
#22309