Finite Group Databasebeta

← #11775425

Subgroups — #11775425

Order 1152.

562 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 562 conjugacy classes of subgroups — too many to draw. Only its 56 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#10596187C211yesmaximal, characteristic
2#10593737C211yesmaximal, characteristic, complemented
3#10593731C211yesmaximal, characteristic, complemented
4#10590209C214yesmaximal, complemented
5C2×#3830—21no—
6C32×#127C411yescharacteristic, complemented
7#64147—21no—
8#64147C2212yes—
9#64145—21no—
10D4×C3⋊Dic3—21no—
11D4×C3⋊Dic3C412yescomplemented
12C42×C3⋊D3C2211yescharacteristic
13#64078C411yescharacteristic, complemented
14#63781—21no—
15#63781—21no—
16#63781C2212yes—
17#63779—21no—
18#63778C2212yes—
19#63777—21no—
20#5716—62no—
21C22×#157—22no—
22C2×C32×D4—21no—
23C2×C32×D4—21no—
24C2×C32×D4C2×C412yes—
25C2×#638—22no—
26C22×C3⋊Dic3—22no—
27#3830—44no—
28C2×C4×C3⋊D3D411yescharacteristic
29C2×C4×C3⋊D3D411yescharacteristic
30C2×C4×C3⋊D3C2311yescharacteristic
31C2×#634—21no—
32C2×#622—22no—
33C32×C42C2×C411yescharacteristic
34#3757—22no—
35#3757—22no—
36C4⋊(C3⋊Dic3)—21no—
37C4⋊(C3⋊Dic3)C2×C412yes—
38C4×C3⋊Dic3C2×C411yescharacteristic
39C4×C3⋊Dic3D411yescharacteristic
40C4×C3⋊Dic3D411yescharacteristic
41#1514—91nomaximal, Sylow
42C2×#237—64no—
43C3×#127—22no—
44#938—64no—
45#938—64no—
46#936—64no—
47D4×Dic3—64no—
48D4×Dic3—64no—
49C42×D3—62no—
50#869—62no—
51C23×C32—22no—
52C22×C3⋊D3C2×D411yescharacteristic
53C2×#157—42no—
54C2×#157—42no—
55C2×#157—42no—
56C32×D4—42no—
57C32×D4—42no—
58C32×D4—42no—
59C2×C32×C4C22⋊C411yescharacteristic
60C2×C32×C4C22⋊C411yescharacteristic
61C2×C32×C4C22×C411yescharacteristic
62#638—44no—
63C2×C3⋊Dic3—22no—
64C2×C3⋊Dic3—44no—
65C2×C3⋊Dic3C22⋊C411yescharacteristic
66C2×C3⋊Dic3C22⋊C411yescharacteristic
67C2×C3⋊Dic3C2×D411yescharacteristic
68C4×C3⋊D3—22no—
69C4×C3⋊D3—41no—
70C4×C3⋊D3—41no—
71#634—42no—
72#622—42no—
73#532—91no—
74#432—91no—
75#383—91no—
76#327—94no—
77C2×C3×D4—24no—
78C2×C3×D4—24no—
79C2×C3×D4—24no—
80C2×#67—68no—
81C22×Dic3—68no—
82#237—1216no—
83C2×C4×D3—62no—
84C2×C4×D3—62no—
85C2×C4×D3—62no—
86C2×Dic6—64no—
87C3×C42—22no—
88#217—68no—
89#217—68no—
90C4⋊Dic3—64no—
91C4⋊Dic3—64no—
92C4×Dic3—62no—
93C4×Dic3—62no—
94C4×Dic3—62no—
95C22×C32—42no—
96C22×C32—42no—
97C22×C32—42no—
98C22×C32C2×C22⋊C411yescharacteristic
99C2×C3⋊D3—21no—
100C2×C3⋊D3—21no—
101C2×C3⋊D3AGL(1,ℤ/8)12yes—
102#157—82no—
103C32×C4—21no—
104C32×C4—21no—
105C32×C4—21no—
106C3⋊Dic3—21no—
107C3⋊Dic3—21no—
108C3⋊Dic3—21no—
109C3⋊Dic3—42no—
110C2×#41—181no—
111C4⋊Q8—91no—
112#127#15711yescharacteristic, complemented
113#124—181no—
114#121—92no—
115#121—181no—
116C4×D4—92no—
117C4×D4—181no—
118C2×C42—91no—
119C4⋊C8—181no—
120C22⋊C8—92no—
121#97—181no—
122#95—92no—
123#95—181no—
124#95—181no—
125C23×C3—28no—
126C22×D3—62no—
127C3×D4—48no—
128C3×D4—48no—
129C3×D4—48no—
130C2×C3×C4—22no—
131C2×C3×C4—22no—
132C2×C3×C4—22no—
133#67—1216no—
134C2×Dic3—62no—
135C2×Dic3—62no—
136C2×Dic3—62no—
137C2×Dic3—68no—
138C2×Dic3—1216no—
139C4×D3—68no—
140C4×D3—124no—
141C4×D3—124no—
142Dic6—128no—
143C2×C32—82no—
144C2×C32#41011yescharacteristic
145C2×C32#41811yescharacteristic
146C2×C32#42111yescharacteristic
147C3⋊D3—22no—
148#41—364no—
149C2×Q8—181no—
150C2×D4—21no—
151C2×D4—21no—
152C2×D4—182no—
153C2×D4C2×#15712yes—
154C22×C4—91no—
155C22×C4—91no—
156C22×C4—91no—
157C22×C4—182no—
158C22×C4—182no—
159C2×C8—182no—
160C4⋊C4—92no—
161C4⋊C4—181no—
162C22⋊C4—182no—
163C22⋊C4—182no—
164C42—91no—
165C42—91no—
166C42—91no—
167C42C2×#15711yescharacteristic
168C22×C3—22no—
169C22×C3—48no—
170C22×C3—48no—
171C22×C3—48no—
172C2×D3—64no—
173C2×D3—122no—
174C2×D3—122no—
175C3×C4—24no—
176C3×C4—24no—
177C3×C4—24no—
178Dic3—64no—
179Dic3—122no—
180Dic3—122no—
181Dic3—128no—
182C32#151411yescharacteristic, complemented, Sylow
183C23—22no—
184C23—91no—
185Q8—362no—
186D4—42no—
187D4—42no—
188D4—42no—
189D4—364no—
190C2×C4—91no—
191C2×C4—91no—
192C2×C4—91no—
193C2×C4—182no—
194C2×C4—182no—
195C2×C4—361no—
196C2×C4—361no—
197C2×C4—364no—
198C2×C4—362no—
199C2×C4—362no—
200C2×C4—362no—
201C2×C4C22⋊#15711yescharacteristic
202C2×C4C22⋊#15711yescharacteristic
203C2×C4C22×#15711yescharacteristic
204C8—362no—
205C2×C3—22no—
206C2×C3—22no—
207C2×C3—22no—
208C2×C3—88no—
209D3—124no—
210C22—42no—
211C22—42no—
212C22—42no—
213C22—92no—
214C22—181no—
215C22—181no—
216C22C2×C22⋊#15711yescharacteristic
217C4—21no—
218C4—21no—
219C4—21no—
220C4—181no—
221C4—181no—
222C4—181no—
223C4—362no—
224C4—722no—
225C3—22no—
226C2—82no—
227C2—182no—
228C2#1059381411yescharacteristic
229C2#1059381611yescharacteristic
230C2#1059381811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×#127C4
socleC22×C32C2×C22⋊C4
prime radical#10596187C2
cosocleC2×C4×C3⋊D3C23
hypercenter#127#157
hypocenterC32#1514
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
2. #10593737C2semidirect
3. #10593731C2semidirect
4. #10590209C2semidirect
6. C32×#127C4semidirect
11. D4×C3⋊Dic3C4semidirect
13. #64078C4semidirect
112. #127#157semidirect
182. C32#1514semidirect

Maximal subgroups

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

subgroupindex
#105961872
#105937372
#105937312
#105902092
#15149