Finite Group Databasebeta

← #11798925

Subgroups — #11798925

Order 1152.

294 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 43 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
1C2×#63735C212yesmaximal
2#10590905C211yesmaximal, characteristic, complemented
3#10590740C211yesmaximal, characteristic
4#10590177C211yesmaximal, characteristic, complemented
5#10590062C212yesmaximal, complemented
6C2×C3×Dic12—21no—
7#63898—21no—
8#63873—21no—
9C2×#3718C2212yes—
10C2×#3713C2211yescharacteristic
11C2×#3708C2212yes—
12#63735—24no—
13C8×C3⋊Dic3C2211yescharacteristic
14C3×#821—21no—
15#63576C2211yescharacteristic
16#5183—61no—
17#4756—61no—
18C2×C3×D12—21no—
19C2×C3×Dic6—22no—
20C2×D3×Dic3—41no—
21C2×C32×C8D411yescharacteristic
22C4×C3⋊Dic3D411yescharacteristic
23C2×C3⋊(C3⋊C8)C2311yescharacteristic
24C3×C4⋊Dic3—21no—
25C3×Dic12—42no—
26#3724—41no—
27#3724—41no—
28(C2×D3)⋊Dic3—41no—
29#3718—22no—
30#3718—22no—
31#3713—21no—
32#3713D412yes—
33#3708—22no—
34#2208—91nomaximal, Sylow
35C2×C3×Q16—61no—
36#944—62no—
37C2×#216—62no—
38D4×Dic3—61no—
39C2×#213—61no—
40C2×Dic12—21no—
41#893—61no—
42C3×#102—61no—
43#821—21no—
44C8×Dic3—61no—
45C8×Dic3—61no—
46#807—61no—
47C22×C3×D3—41no—
48C2×C32×C4C2×D411yescharacteristic
49C2×C3⋊Dic3D811yescharacteristic
50C2×C3⋊Dic3D811yescharacteristic
51C2×C3×Dic3—41no—
52C2×C3×Dic3—42no—
53C3×D12—22no—
54C3×D12—41no—
55C3×Dic6—42no—
56C3×Dic6—42no—
57D3×Dic3—82no—
58C32×C8—21no—
59C3⋊(C3⋊C8)C2×D411yescharacteristic
60C3⋊(C3⋊C8)#4111yescharacteristic
61C2×SD32—92no—
62#494—91no—
63C4×D8—91no—
64C4⋊C16—91no—
65#358—92no—
66C2×C3×Q8—62no—
67C2×C3×D4—61no—
68C22×Dic3—121no—
69C2×D12—21no—
70C2×C4×D3—121no—
71C2×Dic6—22no—
72C3×Q16—122no—
73C2×C3×C8—21no—
74C2×C3×C8—21no—
75C3×C4⋊C4—61no—
76#217—121no—
77#216—122no—
78#216—122no—
79#213—62no—
80#213—62no—
81(C2×D3)⋊C4—121no—
82C4⋊Dic3—21no—
83Dic3⋊C4—122no—
84Dic3⋊C4—122no—
85C4×Dic3—61no—
86C4×Dic3—61no—
87C2×C3⋊C8—61no—
88C2×C3⋊C8—61no—
89Dic12—42no—
90C22×C32C2×D811yescharacteristic
91C2×C3×D3—42no—
92C2×C3×D3—81no—
93C2×C3×D3—81no—
94C32×C4#12111yescharacteristic
95C32×C4AGL(1,ℤ/8)11yescharacteristic
96C3⋊Dic3—21no—
97C3⋊Dic3SD3212yescomplemented
98C3×Dic3—82no—
99C3×Dic3—81no—
100C2×Q16—61no—
101C2×Q16—92no—
102C2×D8—91no—
103C4⋊Q8—181no—
104C4×D4—181no—
105SD32—184no—
106C2×C16—92no—
107#107—91no—
108#102—61no—
109C4×C8—91no—
110C23×C3—121no—
111C22×D3—41no—
112C3×Q8—122no—
113C3×Q8—122no—
114C3×D4—62no—
115C3×D4—121no—
116C2×C3×C4—21no—
117C2×C3×C4—21no—
118C2×C3×C4—122no—
119C2×C3×C4—121no—
120C2×Dic3—42no—
121C2×Dic3—41no—
122C2×Dic3—61no—
123C2×Dic3—61no—
124C2×Dic3—61no—
125C2×Dic3—61no—
126C2×Dic3—242no—
127D12—22no—
128D12—41no—
129C4×D3—242no—
130Dic6—42no—
131Dic6—42no—
132C3×C8—22no—
133C3×C8—41no—
134C3⋊C8—61no—
135C3⋊C8—61no—
136C3⋊C8—61no—
137C3⋊C8—61no—
138C2×C32#45911yescharacteristic
139C2×C32C2×SD3211yescharacteristic
140C2×C32#51011yescharacteristic
141C3×D3—82no—
142C2×Q8—62no—
143C2×D4—61no—
144C22×C4—361no—
145Q16—122no—
146Q16—182no—
147Q16—182no—
148D8—92no—
149D8—181no—
150C2×C8—91no—
151C2×C8GO+(4,𝔽2)11yescharacteristic
152C4⋊C4—61no—
153C4⋊C4—361no—
154C4⋊C4—361no—
155C22⋊C4—361no—
156C42—91no—
157C16—182no—
158C22×C3—21no—
159C22×C3—21no—
160C22×C3—122no—
161C22×C3—241no—
162C22×C3—241no—
163C2×D3—42no—
164C2×D3—81no—
165C2×D3—81no—
166C3×C4—21no—
167C3×C4—21no—
168C3×C4—21no—
169C3×C4—21no—
170C3×C4—241no—
171C3×C4—242no—
172Dic3—62no—
173Dic3—62no—
174Dic3—62no—
175Dic3—82no—
176Dic3—81no—
177Dic3—121no—
178C32#220811yescharacteristic, complemented, Sylow
179C23—121no—
180Q8—122no—
181Q8—122no—
182D4—62no—
183D4—121no—
184C2×C4—91no—
185C2×C4—91no—
186C2×C4—121no—
187C2×C4—122no—
188C2×C4—722no—
189C2×C4C2×GO+(4,𝔽2)11yescharacteristic
190C8—21no—
191C8—91no—
192C8—91no—
193C2×C3—21no—
194C2×C3—21no—
195C2×C3—21no—
196C2×C3—21no—
197C2×C3—21no—
198C2×C3—21no—
199C2×C3—242no—
200D3—82no—
201C22—122no—
202C22—241no—
203C22—241no—
204C22#6422511yescharacteristic
205C4—92no—
206C4—181no—
207C4—242no—
208C4—241no—
209C4#6423011yescharacteristic
210C4#6423611yescharacteristic
211C3—21no—
212C3—21no—
213C2—242no—
214C2#1059327811yescharacteristic
215C2#1059327911yescharacteristic
216C2#1059342611yescharacteristic
subgroupG/H
centerC22#64225
commutator, cosocleC2×C3⋊(C3⋊C8)C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC22×C32C2×D8
prime radicalC2×#3713C22
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#2208
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. #10590905C2semidirect
4. #10590177C2semidirect
5. #10590062C2semidirect
97. C3⋊Dic3SD32semidirect
178. C32#2208semidirect

Maximal subgroups

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

subgroupindex
C2×#637352
#105909052
#105907402
#105901772
#105900622
#22089