Finite Group Databasebeta

← #11791401

Subgroups — #11791401

Order 1152.

646 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 646 conjugacy classes of subgroups — too many to draw. Only its 74 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#10596196C211yesmaximal, characteristic
2C2×#63785C214yesmaximal, complemented
3C4×C4⋊#157C211yesmaximal, characteristic, complemented
4C4×#3788C211yesmaximal, characteristic, complemented
5C2×#3832C2212yes—
6C2×C4⋊#157—21no—
7C2×C4×#157C2212yes—
8C2×#3788C2212yes—
9C32×C4⋊Q8C411yescharacteristic, complemented
10#64156C412yescomplemented
11#64104—21no—
12#64104—21no—
13#64102—21no—
14#64102—21no—
15#64083C411yescharacteristic, complemented
16C42×C3⋊D3C2211yescharacteristic
17#63785—28no—
18#63781—21no—
19#63777—21no—
20C4×#622—21no—
21#5725—62no—
22C22×#157—22no—
23C2×C32×Q8C2×C412yes—
24#3832—24no—
25#3832—24no—
26C2×C4⋊(C3⋊D3)—22no—
27C2×C4⋊(C3⋊D3)—21no—
28C2×C4⋊(C3⋊D3)—21no—
29C2×C4⋊(C3⋊D3)C2×C412yes—
30C2×C4×C3⋊D3—22no—
31C2×C4×C3⋊D3D411yescharacteristic
32C2×C4×C3⋊D3D411yescharacteristic
33C2×C4×C3⋊D3C2311yescharacteristic
34C2×#622—22no—
35C4⋊#157—24no—
36C4×#157—24no—
37#3788—22no—
38#3788D414yescomplemented
39C32×C4⋊C4—21no—
40C32×C4⋊C4—21no—
41C32×C42C2×C411yescharacteristic
42#3752—22no—
43#3752—22no—
44C4×C3⋊Dic3C2×C411yescharacteristic
45C4×C3⋊Dic3D411yescharacteristic
46C4×C3⋊Dic3D411yescharacteristic
47#1980—91nomaximal, Sylow
48C2×#239—64no—
49C3×C4⋊Q8—22no—
50#947—64no—
51#895—64no—
52#895—64no—
53#893—64no—
54#893—64no—
55#874—62no—
56C42×D3—62no—
57C22×C3⋊D3—22no—
58C22×C3⋊D3C2×D411yescharacteristic
59C2×#157—24no—
60C2×#157—42no—
61C2×#157—42no—
62C32×Q8—24no—
63C2×C32×C4—22no—
64C2×C32×C4C22⋊C411yescharacteristic
65C2×C32×C4C22⋊C411yescharacteristic
66C2×C32×C4C22×C411yescharacteristic
67C2×C3⋊Dic3C22⋊C411yescharacteristic
68C2×C3⋊Dic3C22⋊C411yescharacteristic
69C2×C3⋊Dic3C2×D411yescharacteristic
70C4⋊(C3⋊D3)—24no—
71C4⋊(C3⋊D3)—42no—
72C4⋊(C3⋊D3)—42no—
73C4⋊(C3⋊D3)—42no—
74C4⋊(C3⋊D3)—42no—
75C4×C3⋊D3—22no—
76C4×C3⋊D3—41no—
77C4×C3⋊D3—44no—
78C4×C3⋊D3C2×D412yes—
79C4×C3⋊D3#4112yes—
80#622—24no—
81#532—91no—
82C2×#104—94no—
83C4×M16—91no—
84C4×C4⋊C4—91no—
85C2×C3×Q8—24no—
86#239—128no—
87#239—128no—
88C2×D12—64no—
89C2×D12—64no—
90C2×D12—64no—
91C2×D12—68no—
92C2×C4×D3—62no—
93C2×C4×D3—62no—
94C2×C4×D3—62no—
95C2×C4×D3—68no—
96C3×C4⋊C4—24no—
97C3×C4⋊C4—24no—
98C3×C42—22no—
99(C2×D3)⋊C4—68no—
100(C2×D3)⋊C4—68no—
101C4×Dic3—62no—
102C4×Dic3—62no—
103C4×Dic3—62no—
104C22×C32C2×C22⋊C411yescharacteristic
105C2×C3⋊D3—21no—
106C2×C3⋊D3—21no—
107C2×C3⋊D3—42no—
108C2×C3⋊D3—42no—
109C2×C3⋊D3—42no—
110C2×C3⋊D3#12411yescharacteristic
111C2×C3⋊D3#12711yescharacteristic
112#157—44no—
113C32×C4—21no—
114C32×C4—42no—
115C32×C4#10412yescomplemented
116C32×C4C4×D412yes—
117C3⋊Dic3—21no—
118C3⋊Dic3—21no—
119C3⋊Dic3#12112yes—
120C2×#41—92no—
121C2×M16—92no—
122C4⋊Q8#15711yescharacteristic, complemented
123#127—91no—
124#124—92no—
125#121—181no—
126#121—181no—
127C4×D4—181no—
128C4×D4—181no—
129C2×C4⋊C4—181no—
130C2×C42—91no—
131C2×C42—92no—
132#104—188no—
133#97—181no—
134C4×C8—181no—
135#95—181no—
136C22×D3—62no—
137C22×D3—68no—
138C3×Q8—48no—
139C2×C3×C4—28no—
140C2×C3×C4—22no—
141C2×C3×C4—22no—
142C2×C3×C4—22no—
143C2×Dic3—62no—
144C2×Dic3—62no—
145C2×Dic3—62no—
146D12—128no—
147D12—128no—
148D12—128no—
149D12—128no—
150D12—128no—
151C4×D3—64no—
152C4×D3—64no—
153C4×D3—124no—
154C4×D3—1216no—
155C4×D3—124no—
156C2×C32#39011yescharacteristic
157C2×C32C2×#10411yescharacteristic
158C2×C32#42111yescharacteristic
159C3⋊D3—21no—
160C3⋊D3—21no—
161C3⋊D3—82no—
162#41—184no—
163#41—184no—
164C2×Q8C2×#15712yes—
165C2×D4—92no—
166C2×D4—182no—
167C2×D4—181no—
168C2×D4—181no—
169C22×C4—91no—
170C22×C4—91no—
171C22×C4—91no—
172C22×C4—182no—
173C22×C4—182no—
174M16—94no—
175M16—182no—
176C2×C8—182no—
177C4⋊C4—21no—
178C4⋊C4—21no—
179C4⋊C4—184no—
180C22⋊C4—182no—
181C22⋊C4—182no—
182C42—91no—
183C42—91no—
184C42—91no—
185C42—184no—
186C42C2×#15711yescharacteristic
187C22×C3—22no—
188C2×D3—62no—
189C2×D3—62no—
190C2×D3—122no—
191C2×D3—122no—
192C2×D3—128no—
193C2×D3—128no—
194C2×D3—128no—
195C3×C4—24no—
196C3×C4—24no—
197C3×C4—24no—
198C3×C4—48no—
199Dic3—64no—
200Dic3—122no—
201Dic3—122no—
202C32#198011yescharacteristic, complemented, Sylow
203C23—91no—
204C23—182no—
205Q8—24no—
206D4—184no—
207D4—362no—
208D4—362no—
209D4—362no—
210D4—362no—
211C2×C4—22no—
212C2×C4—91no—
213C2×C4—92no—
214C2×C4—92no—
215C2×C4—91no—
216C2×C4—91no—
217C2×C4—182no—
218C2×C4—184no—
219C2×C4—361no—
220C2×C4—364no—
221C2×C4—362no—
222C2×C4—362no—
223C2×C4C22⋊#15711yescharacteristic
224C2×C4C22⋊#15711yescharacteristic
225C2×C4C22×#15711yescharacteristic
226C8—184no—
227C2×C3—22no—
228C2×C3—22no—
229C2×C3—22no—
230D3—122no—
231D3—122no—
232D3—248no—
233C22—91no—
234C22—91no—
235C22—181no—
236C22—181no—
237C22—362no—
238C22—362no—
239C22—362no—
240C22C2×C22⋊#15711yescharacteristic
241C4—21no—
242C4—42no—
243C4—92no—
244C4—181no—
245C4—181no—
246C4—364no—
247C4#6378512yescomplemented
248C4D4×#15712yes—
249C3—22no—
250C2—181no—
251C2—181no—
252C2—722no—
253C2#1059382711yescharacteristic
254C2C2×#6378511yescharacteristic
255C2#1059383111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×C4⋊Q8C4
socleC22×C32C2×C22⋊C4
prime radical#10596196C2
cosocleC2×C4×C3⋊D3C23
hypercenterC4⋊Q8#157
hypocenterC32#1980
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#63785C2semidirect
3. C4×C4⋊#157C2semidirect
4. C4×#3788C2semidirect
9. C32×C4⋊Q8C4semidirect
10. #64156C4semidirect
15. #64083C4semidirect
38. #3788D4semidirect
115. C32×C4#104semidirect
122. C4⋊Q8#157semidirect
202. C32#1980semidirect
247. C4#63785semidirect

Maximal subgroups

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

subgroupindex
#105961962
C2×#637852
C4×C4⋊#1572
C4×#37882
#19809