Finite Group Databasebeta

← #11796884

Subgroups — #11796884

Order 1152.

594 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 594 conjugacy classes of subgroups — too many to draw. Only its 64 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×D8×C3⋊D3C211yesmaximal, characteristic
2#10593771C211yesmaximal, characteristic, complemented
3#10593762C211yesmaximal, characteristic, complemented
4#10590195C214yesmaximal, complemented
5C2×D4×C3⋊D3—21no—
6#64283—21no—
7C2×C32×D8C411yescharacteristic
8C2×#3753—21no—
9D8×C3⋊D3—21no—
10D8×C3⋊D3—21no—
11D8×C3⋊D3C412yes—
12D8×C3⋊D3C2212yes—
13C2×#3745C411yescharacteristic
14C2×C8×C3⋊D3C2211yescharacteristic
15#63773—21no—
16#63771—21no—
17#63770C2212yescomplemented
18#63765C2212yescomplemented
19#63764—21no—
20C2×D3×D8—62no—
21C23×C3⋊D3—41no—
22C2×C32×D4—21no—
23C2×#638—41no—
24D4×C3⋊D3—22no—
25D4×C3⋊D3—22no—
26D4×C3⋊D3—41no—
27D4×C3⋊D3—41no—
28C2×C4⋊(C3⋊D3)—21no—
29C2×C4×C3⋊D3D411yescharacteristic
30#3792—41no—
31#3788—22no—
32#3787—41no—
33C32×D8—21no—
34C32×D8C2×C412yes—
35C2×C32×C8C2×C411yescharacteristic
36#3753—22no—
37#3753—22no—
38C2×C3⋊(C3⋊C8)D411yescharacteristic
39#3745—21no—
40#3745C2×C412yes—
41C8×C3⋊D3C2×C411yescharacteristic
42C8×C3⋊D3D411yescharacteristic
43C8×C3⋊D3D411yescharacteristic
44C8×C3⋊D3C2311yescharacteristic
45#3708—22no—
46C2×#361—91nomaximal, Sylow
47C2×D3×D4—64no—
48C2×C3×D8—22no—
49C2×#213—64no—
50D3×D8—64no—
51D3×D8—64no—
52D3×D8—64no—
53D3×D8—64no—
54C2×D24—62no—
55C2×D3×C8—62no—
56C23×C32—41no—
57C22×C3⋊D3—41no—
58C22×C3⋊D3—42no—
59C22×C3⋊D3—42no—
60C22×C3⋊D3—84no—
61C22×C3⋊D3SD1611yescharacteristic
62C32×D4—22no—
63C32×D4—41no—
64C2×C32×C4C22⋊C411yescharacteristic
65#638—42no—
66#638—42no—
67C2×C3⋊Dic3D811yescharacteristic
68C4⋊(C3⋊D3)—22no—
69C4⋊(C3⋊D3)—41no—
70C4×C3⋊D3C22⋊C411yescharacteristic
71C4×C3⋊D3D811yescharacteristic
72C4×C3⋊D3SD1611yescharacteristic
73C4×C3⋊D3C2×D411yescharacteristic
74#622—42no—
75C32×C8C22⋊C411yescharacteristic
76C32×C8C22×C411yescharacteristic
77C3⋊(C3⋊C8)C22⋊C411yescharacteristic
78C3⋊(C3⋊C8)C2×D411yescharacteristic
79C22×D8—91no—
80C2×M32—91no—
81C2×#108—91no—
82#361—94no—
83C23×D3—124no—
84C2×C3×D4—24no—
85C2×#67—124no—
86D3×D4—68no—
87D3×D4—68no—
88D3×D4—124no—
89D3×D4—124no—
90C2×D12—64no—
91C2×C4×D3—62no—
92C3×D8—24no—
93C3×D8—24no—
94C2×C3×C8—22no—
95#213—68no—
96#213—68no—
97C2×C3⋊C8—62no—
98D24—64no—
99D24—64no—
100D3×C8—62no—
101D3×C8—62no—
102D3×C8—62no—
103D3×C8—62no—
104C22×C32—42no—
105C22×C32—82no—
106C22×C32#10211yescharacteristic
107C2×C3⋊D3—22no—
108C2×C3⋊D3—42no—
109C2×C3⋊D3—84no—
110C2×C3⋊D3—82no—
111C2×C3⋊D3—84no—
112C2×C3⋊D3#10211yescharacteristic
113C2×C3⋊D3C2×SD1611yescharacteristic
114C32×C4#10211yescharacteristic
115C32×C4C2×C22⋊C411yescharacteristic
116C3⋊Dic3#10211yescharacteristic
117C3⋊Dic3C2×D811yescharacteristic
118C22×D4—181no—
119C2×D8—92no—
120C2×D8—92no—
121C2×D8—91no—
122C2×D8—181no—
123C2×D8—181no—
124C2×D8—181no—
125C2×D8#15711yescharacteristic
126C2×M16—181no—
127C22×C8—91no—
128M32—92no—
129M32—181no—
130C2×C16—181no—
131#108—92no—
132#108—181no—
133C23×C3—44no—
134C22×D3—62no—
135C22×D3—128no—
136C22×D3—128no—
137C22×D3—124no—
138C22×D3—2416no—
139C3×D4—28no—
140C3×D4—44no—
141C2×C3×C4—22no—
142#67—128no—
143#67—128no—
144C2×Dic3—62no—
145D12—68no—
146D12—124no—
147C4×D3—62no—
148C4×D3—62no—
149C4×D3—62no—
150C4×D3—62no—
151C3×C8—22no—
152C3×C8—22no—
153C3⋊C8—62no—
154C3⋊C8—62no—
155C2×C32—21no—
156C2×C32—82no—
157C2×C32C2×#10211yescharacteristic
158C3⋊D3—21no—
159C3⋊D3—82no—
160C3⋊D3#36112yescomplemented
161C24—361no—
162C2×D4—21no—
163C2×D4—182no—
164C2×D4—182no—
165C2×D4—181no—
166C2×D4—361no—
167C2×D4—361no—
168C2×D4—361no—
169C22×C4—91no—
170D8—21no—
171D8—92no—
172D8—182no—
173D8—182no—
174D8—181no—
175D8C2×#15712yes—
176M16—182no—
177M16—361no—
178C2×C8—91no—
179C2×C8—91no—
180C2×C8—91no—
181C2×C8—91no—
182C2×C8—91no—
183C2×C8—361no—
184C2×C8C2×#15711yescharacteristic
185C16—182no—
186C22×C3—22no—
187C22×C3—48no—
188C22×C3—88no—
189C2×D3—62no—
190C2×D3—62no—
191C2×D3—68no—
192C2×D3—128no—
193C2×D3—2416no—
194C2×D3—2416no—
195C2×D3—248no—
196C3×C4—22no—
197C3×C4—22no—
198Dic3—62no—
199Dic3—62no—
200C32C2×#36111yescharacteristic, complemented, Sylow
201C23—41no—
202C23—91no—
203C23—362no—
204C23—362no—
205C23—361no—
206C23—724no—
207D4—22no—
208D4—41no—
209D4—182no—
210D4—362no—
211D4—362no—
212D4—361no—
213C2×C4—91no—
214C2×C4—91no—
215C2×C4—91no—
216C2×C4—91no—
217C2×C4—91no—
218C2×C4C22⋊#15711yescharacteristic
219C8—91no—
220C8—91no—
221C8—362no—
222C8C22⋊#15711yescharacteristic
223C8C22×#15711yescharacteristic
224C2×C3—24no—
225C2×C3—22no—
226C2×C3—88no—
227D3—64no—
228D3—64no—
229D3—248no—
230C22—42no—
231C22—82no—
232C22—91no—
233C22—91no—
234C22—182no—
235C22—362no—
236C22—722no—
237C22—724no—
238C22—724no—
239C22#6378211yescharacteristic
240C4—91no—
241C4—91no—
242C4#6378211yescharacteristic
243C4C2×C22⋊#15711yescharacteristic
244C3—22no—
245C2—21no—
246C2—82no—
247C2—92no—
248C2—181no—
249C2—722no—
250C2C2×#6378211yescharacteristic
subgroupG/H
centerC2C2×#63782
commutatorC32×C8C22×C4
FrattiniC8C22×#157
FittingC2×C32×D8C4
socleC2×C32C2×#102
prime radicalC2×D8×C3⋊D3C2
cosocleC8×C3⋊D3C23
hypercenterC2×D8#157
hypocenterC32C2×#361
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
2. #10593771C2semidirect
3. #10593762C2semidirect
4. #10590195C2semidirect
17. #63770C22semidirect
18. #63765C22semidirect
160. C3⋊D3#361semidirect
200. C32C2×#361semidirect

Maximal subgroups

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

subgroupindex
C2×D8×C3⋊D32
#105937712
#105937622
#105901952
C2×#3619