Finite Group Databasebeta

← #11790590

Subgroups — #11790590

Order 1152.

810 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 810 conjugacy classes of subgroups — too many to draw. Only its 90 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×#64102C211yesmaximal, characteristic
2C2×#63779C211yesmaximal, characteristic, complemented
3C2×#63778C214yesmaximal, complemented
4C2×#63777C211yesmaximal, characteristic, complemented
5C22×C4⋊(C3⋊D3)C411yescharacteristic
6C22×C4×C3⋊D3C2212yes—
7C22×#622C2212yes—
8C22×#622C2212yes—
9C2×C32×C4⋊C4C411yescharacteristic
10C2×#3752C412yes—
11C2×C4×C3⋊Dic3C2211yescharacteristic
12#64102—22no—
13#64102—22no—
14#63779—22no—
15#63778—28no—
16#63777—22no—
17C2×#893—62no—
18C23×C3⋊D3C2×C412yes—
19C22×C32×C4C2×C412yes—
20C22×C32×C4C2×C411yescharacteristic
21C22×C3⋊Dic3C2×C411yescharacteristic
22C22×C3⋊Dic3C2311yescharacteristic
23C2×C4⋊(C3⋊D3)—24no—
24C2×C4⋊(C3⋊D3)—22no—
25C2×C4×C3⋊D3—22no—
26C2×C4×C3⋊D3—22no—
27C2×C4×C3⋊D3—24no—
28C2×C4×C3⋊D3—24no—
29C2×#622—22no—
30C2×#622—22no—
31C2×#622—24no—
32C2×#622—22no—
33C2×#622D414yescomplemented
34C32×C4⋊C4—22no—
35#3752—24no—
36C4×C3⋊Dic3D412yes—
37C4×C3⋊Dic3D412yes—
38#1955—91nomaximal, Sylow
39C22×D12—62no—
40C22×C4×D3—64no—
41C2×C3×C4⋊C4—22no—
42C2×(C2×D3)⋊C4—64no—
43C2×C4×Dic3—62no—
44#893—68no—
45#893—68no—
46C23×C32C22×C411yescharacteristic
47C22×C3⋊D3—22no—
48C22×C3⋊D3—22no—
49C22×C3⋊D3—24no—
50C22×C3⋊D3—24no—
51C22×C3⋊D3M1614yes—
52C2×C32×C4—22no—
53C2×C32×C4—22no—
54C2×C32×C4—24no—
55C2×C32×C4C22⋊C412yes—
56C2×C3⋊Dic3—22no—
57C2×C3⋊Dic3C22⋊C412yes—
58C2×C3⋊Dic3C2×D411yescharacteristic
59C2×C3⋊Dic3C2×D412yes—
60C2×C3⋊Dic3C2×D411yescharacteristic
61C2×C3⋊Dic3#4112yes—
62C4⋊(C3⋊D3)—28no—
63C4×C3⋊D3—44no—
64C4×C3⋊D3—42no—
65C4×C3⋊D3—42no—
66#622—24no—
67#622—42no—
68C2×C4×D4—91no—
69C2×C4⋊C8—91no—
70C2×C22⋊C8—94no—
71C2×#97—91no—
72C23×D3—64no—
73C22×C3×C4—22no—
74C22×C3×C4—24no—
75C22×Dic3—62no—
76C22×Dic3—62no—
77C2×D12—68no—
78C2×D12—616no—
79C2×C4×D3—68no—
80C2×C4×D3—68no—
81C2×C4×D3—128no—
82C2×C4×D3—128no—
83C3×C4⋊C4—28no—
84(C2×D3)⋊C4—616no—
85C4×Dic3—64no—
86C4×Dic3—64no—
87C22×C32C2×C22⋊C411yescharacteristic
88C22×C32C4×D412yes—
89C22×C32C2×M1612yes—
90C22×C32#13112yes—
91C2×C3⋊D3—24no—
92C2×C3⋊D3—28no—
93C2×C3⋊D3—42no—
94C2×C3⋊D3—42no—
95C2×C3⋊D3—44no—
96C32×C4—22no—
97C32×C4—42no—
98C3⋊Dic3—22no—
99C3⋊Dic3#12112yes—
100C3⋊Dic3#12411yescharacteristic
101C3⋊Dic3#12711yescharacteristic
102C22×D4—91no—
103C23×C4—92no—
104C22×C8—92no—
105C22×C8—92no—
106C4×D4—182no—
107C4×D4—182no—
108C2×C4⋊C4#15711yescharacteristic
109C2×C22⋊C4—92no—
110C2×C42—91no—
111C4⋊C8—182no—
112C22⋊C8—188no—
113#97—182no—
114C23×C3—22no—
115C22×D3—68no—
116C22×D3—68no—
117C22×D3—68no—
118C22×D3—128no—
119C22×D3—128no—
120C2×C3×C4—28no—
121C2×C3×C4—28no—
122C2×C3×C4—24no—
123C2×C3×C4—48no—
124C2×Dic3—62no—
125C2×Dic3—62no—
126C2×Dic3—64no—
127C2×Dic3—64no—
128C2×Dic3—64no—
129C2×Dic3—124no—
130D12—632no—
131C4×D3—1216no—
132C4×D3—128no—
133C4×D3—128no—
134C2×C32#39011yescharacteristic
135C2×C32#40711yescharacteristic
136C2×C32#40811yescharacteristic
137C2×C32#43514yes—
138C3⋊D3—44no—
139C24—92no—
140C2×D4—184no—
141C2×D4—182no—
142C22×C4—91no—
143C22×C4—91no—
144C22×C4—184no—
145C22×C4—182no—
146C22×C4—182no—
147C22×C4—184no—
148C22×C4C2×#15712yes—
149C22×C4C2×#15711yescharacteristic
150C2×C8—94no—
151C2×C8—182no—
152C2×C8—182no—
153C2×C8—184no—
154C2×C8—182no—
155C4⋊C4—22no—
156C22⋊C4—184no—
157C42—92no—
158C42—92no—
159C22×C3—24no—
160C22×C3—24no—
161C22×C3—24no—
162C22×C3—22no—
163C2×D3—616no—
164C2×D3—1216no—
165C2×D3—128no—
166C2×D3—128no—
167C2×D3—1216no—
168C3×C4—28no—
169C3×C4—48no—
170Dic3—64no—
171Dic3—62no—
172Dic3—62no—
173Dic3—124no—
174C32#195511yescharacteristic, complemented, Sylow
175C23—94no—
176C23—182no—
177C23—184no—
178C23—184no—
179C23—182no—
180C23C22×#15711yescharacteristic
181D4—188no—
182C2×C4—22no—
183C2×C4—24no—
184C2×C4—22no—
185C2×C4—92no—
186C2×C4—92no—
187C2×C4—91no—
188C2×C4—91no—
189C2×C4—92no—
190C2×C4—182no—
191C2×C4—364no—
192C2×C4—362no—
193C2×C4—362no—
194C2×C4C22⋊#15712yes—
195C8—184no—
196C8—362no—
197C2×C3—22no—
198C2×C3—22no—
199C2×C3—22no—
200C2×C3—28no—
201D3—1216no—
202C22—184no—
203C22—188no—
204C22—362no—
205C22—362no—
206C22—364no—
207C22#6428312yes—
208C22D4×#15712yes—
209C22#6428912yes—
210C22C2×C22⋊#15711yescharacteristic
211C4—22no—
212C4—42no—
213C4—92no—
214C4—91no—
215C4—91no—
216C4—182no—
217C3—22no—
218C2—364no—
219C2#1059375114yes—
220C2#1059380211yescharacteristic
221C2#1059382711yescharacteristic
222C2#1059383411yescharacteristic
subgroupG/H
center, FrattiniC23C22×#157
commutator, socleC23×C32C22×C4
FittingC2×C32×C4⋊C4C4
prime radicalC22×C4⋊(C3⋊D3)C4
cosocleC22×C3⋊Dic3C23
hypercenterC2×C4⋊C4#157
hypocenterC32#1955
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#63779C2semidirect
3. C2×#63778C2semidirect
4. C2×#63777C2semidirect
33. C2×#622D4semidirect
174. C32#1955semidirect

Maximal subgroups

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

subgroupindex
C2×#641022
C2×#637792
C2×#637782
C2×#637772
#19559