Finite Group Databasebeta

← #11800000

Subgroups — #11800000

Order 1152.

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

normal subgroups only

This group has 250 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#10591167C211yesmaximal, characteristic
2#10591143C211yesmaximal, characteristic, complemented
3#10590201C211yesmaximal, characteristic, complemented
4#10590067C212yesmaximal, complemented
5#10590065C212yesmaximal, complemented
6C2×#3748C2211yescharacteristic
7C3×#930—21no—
8C2×C3×#208—21no—
9C2×#3713C2211yescharacteristic
10#63773C2212yes—
11#63578—21no—
12#63578C2212yes—
13#63574C2211yescharacteristic
14#63562—21no—
15#5124—61no—
16#5039—61no—
17C22×C32×C4D411yescharacteristic
18C2×C3×#67—41no—
19C2×C3×D12—21no—
20#3748—22no—
21C2×C3⋊(C3⋊C8)D411yescharacteristic
22C2×C3⋊(C3⋊C8)C2311yescharacteristic
23C3×(C2×D3)⋊C4—41no—
24C3×C4⋊Dic3—21no—
25C3×#208—22no—
26C3×#208—41no—
27C2×C3×C3⋊C8—41no—
28#3713—22no—
29#3708—22no—
30#2238—91nomaximal, Sylow
31C2×C3×M16—61no—
32C3×#121—61no—
33C2×#213—61no—
34#930—21no—
35C2×#208—21no—
36C2×#208—61no—
37C2×#208—61no—
38#832—61no—
39#822—62no—
40#822—62no—
41#809—61no—
42#808—61no—
43C23×C32SD1611yescharacteristic
44C22×C3×D3—41no—
45C2×C32×C4—21no—
46C2×C32×C4—21no—
47C2×C32×C4SD1611yescharacteristic
48C2×C32×C4C2×D411yescharacteristic
49C3×#67—82no—
50C2×C3×Dic3—41no—
51C3×D12—41no—
52C3×D12—41no—
53C3⋊(C3⋊C8)—21no—
54C3⋊(C3⋊C8)#4112yes—
55C3×C3⋊C8—42no—
56#469—91no—
57#430—91no—
58#365—92no—
59#361—92no—
60#349—91no—
61C2×C3×D4—61no—
62C2×C3×D4—121no—
63C22×C3×C4—21no—
64C22×C3×C4—21no—
65C2×#67—41no—
66C2×D12—21no—
67C3×M16—62no—
68C3×M16—121no—
69C2×C3×C8—121no—
70C3×C4⋊C4—61no—
71C3×C22⋊C4—121no—
72#213—122no—
73(C2×D3)⋊C4—41no—
74C4⋊Dic3—21no—
75#208—22no—
76#208—41no—
77#208—62no—
78#208—62no—
79#208—122no—
80C2×C3⋊C8—41no—
81C2×C3⋊C8—61no—
82C2×C3⋊C8—61no—
83C2×C3⋊C8—61no—
84C2×C3⋊C8—61no—
85C22×C32—21no—
86C22×C32—41no—
87C22×C32C2×SD1611yescharacteristic
88C2×C3×D3—81no—
89C2×C3×D3—81no—
90C2×C3×D3—81no—
91C32×C4—21no—
92C32×C4#12311yescharacteristic
93C32×C4AGL(1,ℤ/8)11yescharacteristic
94C3×Dic3—81no—
95C2×D8—91no—
96C2×M16—61no—
97C2×M16—91no—
98#121—61no—
99M32—92no—
100#108—92no—
101#108—181no—
102#106—91no—
103#102—181no—
104C23×C3—21no—
105C23×C3—21no—
106C23×C3—121no—
107C22×D3—41no—
108C3×D4—121no—
109C3×D4—121no—
110C3×D4—242no—
111C2×C3×C4—21no—
112C2×C3×C4—21no—
113C2×C3×C4—21no—
114C2×C3×C4—21no—
115C2×C3×C4—21no—
116C2×C3×C4—21no—
117C2×C3×C4—21no—
118C2×C3×C4—21no—
119C2×C3×C4—41no—
120C2×C3×C4—41no—
121C2×C3×C4—121no—
122#67—82no—
123C2×Dic3—41no—
124D12—41no—
125D12—41no—
126C3×C8—122no—
127C3⋊C8—42no—
128C3⋊C8—62no—
129C3⋊C8—62no—
130C3⋊C8—62no—
131C3⋊C8—121no—
132C2×C32—21no—
133C2×C32—41no—
134C2×C32#48111yescharacteristic
135C3×D3—161no—
136C2×D4—61no—
137C2×D4—121no—
138C22×C4GO+(4,𝔽2)11yescharacteristic
139D8—182no—
140M16—62no—
141M16—121no—
142M16—182no—
143C2×C8—91no—
144C2×C8—91no—
145C2×C8—121no—
146C4⋊C4—61no—
147C22⋊C4—121no—
148C16—182no—
149C22×C3—21no—
150C22×C3—21no—
151C22×C3—21no—
152C22×C3—21no—
153C22×C3—41no—
154C22×C3—41no—
155C22×C3—41no—
156C22×C3—81no—
157C22×C3—241no—
158C22×C3—241no—
159C22×C3—241no—
160C2×D3—81no—
161C2×D3—81no—
162C2×D3—81no—
163C3×C4—21no—
164C3×C4—21no—
165C3×C4—21no—
166C3×C4—21no—
167C3×C4—21no—
168C3×C4—21no—
169C3×C4—41no—
170C3×C4—241no—
171Dic3—81no—
172C32#223811yescharacteristic, complemented, Sylow
173C23—121no—
174C23#377511yescharacteristic
175D4—121no—
176D4—121no—
177D4—242no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—121no—
181C2×C4#377511yescharacteristic
182C2×C4C2×GO+(4,𝔽2)11yescharacteristic
183C8—92no—
184C8—122no—
185C8—181no—
186C2×C3—21no—
187C2×C3—21no—
188C2×C3—21no—
189C2×C3—21no—
190C2×C3—41no—
191C2×C3—41no—
192C2×C3—41no—
193C2×C3—81no—
194C2×C3—481no—
195D3—161no—
196C22—21no—
197C22—41no—
198C22—241no—
199C22—241no—
200C22—241no—
201C22C2×#377511yescharacteristic
202C4—21no—
203C4—241no—
204C4#6423311yescharacteristic
205C4#6423611yescharacteristic
206C3—21no—
207C3—21no—
208C2—21no—
209C2—41no—
210C2—481no—
211C2#1059349711yescharacteristic
subgroupG/H
centerC2#10593497
commutator, cosocleC2×C3⋊(C3⋊C8)C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC2×C32#481
prime radical#10591167C2
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#2238
LCSG ▷ C2×C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. #10591143C2semidirect
3. #10590201C2semidirect
4. #10590067C2semidirect
5. #10590065C2semidirect
172. C32#2238semidirect

Maximal subgroups

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

subgroupindex
#105911672
#105911432
#105902012
#105900672
#105900652
#22389