Finite Group Databasebeta

← #11799648

Subgroups — #11799648

Order 1152.

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

normal subgroups only

This group has 246 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
1C4×#3713C211yesmaximal, characteristic
2#10590314C211yesmaximal, characteristic, complemented
3C4⋊#3708C211yesmaximal, characteristic, complemented
4#10590069C211yesmaximal, characteristic, complemented
5#10590068C211yesmaximal, characteristic, complemented
6#10590061C211yesmaximal, characteristic
7#10590061C211yesmaximal, characteristic
8C3×C4×D12—21no—
9C3×#870—21no—
10C2×#3713C2211yescharacteristic
11C2×#3708C2211yescharacteristic
12C2×#3708C2211yescharacteristic
13C4×C3⋊(C3⋊C8)C2211yescharacteristic
14#63576C2211yescharacteristic
15#63576C2211yescharacteristic
16#63576C2211yescharacteristic
17#63574—21no—
18#63562—21no—
19#5065—61no—
20C4×#213—61no—
21C2×C3×D12—21no—
22C2×C3×C4×D3—41no—
23C32×C42D411yescharacteristic
24C2×C3⋊(C3⋊C8)D411yescharacteristic
25C2×C3⋊(C3⋊C8)C2311yescharacteristic
26C3×(C2×D3)⋊C4—41no—
27C3×C4⋊Dic3—21no—
28C3×C4⋊Dic3—21no—
29C3×C4⋊Dic3—21no—
30C3×Dic3⋊C4—41no—
31C3×Dic3⋊C4—41no—
32#3713—21no—
33#3713Q812yes—
34#3708—21no—
35#3708—21no—
36#2228—91nomaximal, Sylow
37C3×#125—61no—
38C3×C4×D4—61no—
39C2×#213—61no—
40C4×D12—21no—
41#870—21no—
42#832—61no—
43#809—61no—
44#808—61no—
45#808—61no—
46#807—61no—
47#807—61no—
48#807—61no—
49C4×C3⋊C8—61no—
50C4×C3⋊C8—61no—
51C22×C3×D3—41no—
52C2×C32×C4D811yescharacteristic
53C2×C32×C4D811yescharacteristic
54C2×C32×C4C2×D411yescharacteristic
55C2×C3×Dic3—41no—
56C2×C3×Dic3—41no—
57C2×C3×Dic3—41no—
58C3×D12—22no—
59C3×D12—41no—
60C3×C4×D3—82no—
61C3⋊(C3⋊C8)—21no—
62C3⋊(C3⋊C8)C2×Q811yescharacteristic
63C3⋊(C3⋊C8)#4111yescharacteristic
64#499—91no—
65C4×D8—91no—
66#367—91no—
67#366—91no—
68C4⋊C16—91no—
69#357—91no—
70#357—91no—
71C2×C3×D4—61no—
72C22×C3×C4—121no—
73C2×D12—21no—
74C2×C4×D3—41no—
75C3×C4⋊C4—61no—
76C3×C4⋊C4—61no—
77C3×C4⋊C4—61no—
78C3×C4⋊C4—121no—
79C3×C4⋊C4—121no—
80C3×C22⋊C4—121no—
81C3×C42—21no—
82C3×C42—21no—
83#213—62no—
84#213—62no—
85(C2×D3)⋊C4—41no—
86C4⋊Dic3—21no—
87C4⋊Dic3—21no—
88C4⋊Dic3—21no—
89Dic3⋊C4—41no—
90Dic3⋊C4—41no—
91C2×C3⋊C8—61no—
92C2×C3⋊C8—61no—
93C2×C3⋊C8—61no—
94C2×C3⋊C8—61no—
95C22×C32C2×D811yescharacteristic
96C2×C3×D3—42no—
97C2×C3×D3—81no—
98C2×C3×D3—81no—
99C32×C4—21no—
100C32×C4—21no—
101C32×C4C22⋊Q811yescharacteristic
102C32×C4#13711yescharacteristic
103C3×Dic3—81no—
104C3×Dic3—81no—
105C3×Dic3—81no—
106C2×D8—91no—
107#125—61no—
108C4×D4—61no—
109C2×C16—91no—
110C2×C16—91no—
111#107—91no—
112#107—91no—
113#107—91no—
114#106—181no—
115#102—181no—
116C4×C8—91no—
117C23×C3—121no—
118C22×D3—41no—
119C3×D4—62no—
120C3×D4—121no—
121C2×C3×C4—21no—
122C2×C3×C4—21no—
123C2×C3×C4—21no—
124C2×C3×C4—21no—
125C2×C3×C4—21no—
126C2×C3×C4—21no—
127C2×C3×C4—121no—
128C2×C3×C4—121no—
129C2×C3×C4—121no—
130C2×C3×C4—242no—
131C2×Dic3—41no—
132C2×Dic3—41no—
133C2×Dic3—41no—
134D12—22no—
135D12—41no—
136C4×D3—82no—
137C3⋊C8—61no—
138C3⋊C8—61no—
139C3⋊C8—61no—
140C3⋊C8—61no—
141C3⋊C8—62no—
142C3⋊C8—121no—
143C2×C32#47411yescharacteristic
144C2×C32#50811yescharacteristic
145C2×C32#50911yescharacteristic
146C3×D3—82no—
147C2×D4—61no—
148C22×C4—121no—
149D8—92no—
150D8—181no—
151C2×C8—91no—
152C2×C8—91no—
153C4⋊C4—61no—
154C4⋊C4—61no—
155C4⋊C4—61no—
156C4⋊C4—121no—
157C4⋊C4—121no—
158C22⋊C4—121no—
159C42GO+(4,𝔽2)11yescharacteristic
160C16—181no—
161C16—181no—
162C22×C3—21no—
163C22×C3—21no—
164C22×C3—122no—
165C22×C3—241no—
166C22×C3—241no—
167C2×D3—42no—
168C2×D3—81no—
169C2×D3—81no—
170C3×C4—22no—
171C3×C4—21no—
172C3×C4—21no—
173C3×C4—21no—
174C3×C4—21no—
175C3×C4—41no—
176C3×C4—41no—
177C3×C4—41no—
178C3×C4—241no—
179C3×C4—241no—
180C3×C4—241no—
181Dic3—81no—
182Dic3—81no—
183Dic3—81no—
184C32#222811yescharacteristic, complemented, Sylow
185C23—121no—
186D4—62no—
187D4—121no—
188C2×C4—121no—
189C2×C4—121no—
190C2×C4—121no—
191C2×C4—242no—
192C2×C4#377411yescharacteristic
193C2×C4#377411yescharacteristic
194C2×C4C2×GO+(4,𝔽2)11yescharacteristic
195C8—91no—
196C8—91no—
197C8—181no—
198C2×C3—21no—
199C2×C3—21no—
200C2×C3—21no—
201C2×C3—21no—
202C2×C3—21no—
203C2×C3—21no—
204C2×C3—242no—
205D3—82no—
206C22—122no—
207C22—241no—
208C22—241no—
209C22C2×#377411yescharacteristic
210C4—21no—
211C4—21no—
212C4—241no—
213C4—241no—
214C4—241no—
215C4D32⋊Q811yescharacteristic
216C4#6422611yescharacteristic
217C3—21no—
218C3—21no—
219C2—242no—
220C2#1059333311yescharacteristic
221C2#1059333411yescharacteristic
222C2#1059334711yescharacteristic
subgroupG/H
centerC22C2×#3774
commutator, cosocleC2×C3⋊(C3⋊C8)C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32C2×D8
prime radicalC2×#3713C22
hypercenterC42GO+(4,𝔽2)
hypocenterC32#2228
LCSG ▷ C2×C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
2. #10590314C2semidirect
3. C4⋊#3708C2semidirect
4. #10590069C2semidirect
5. #10590068C2semidirect
184. C32#2228semidirect

Maximal subgroups

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

subgroupindex
C4×#37132
#105903142
C4⋊#37082
#105900692
#105900682
#105900612
#22289