Finite Group Databasebeta

← #11775083

Subgroups — #11775083

Order 1152.

462 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 68 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#10596049C211yesmaximal, characteristic
2C4×C4⋊#157C211yesmaximal, characteristic
3#10593725C211yesmaximal, characteristic
4#10590215C212yesmaximal
5#10590158C212yesmaximal
6C2×C4⋊#157—21no—
7C2×C4×#157—21no—
8C32×C4×Q8C411yescharacteristic, complemented
9#64155C2211yescharacteristic
10#64153C411yescharacteristic, complemented
11#64106C2211yescharacteristic
12#64105—21no—
13#64098—21no—
14#64097C411yescharacteristic, complemented
15#64081—21no—
16C42×C3⋊D3C2211yescharacteristic
17C4×#634—21no—
18C4×#634C411yescharacteristic, complemented
19#63781C2212yes—
20#63779—21no—
21#63778C2212yes—
22C4×#622—21no—
23#5578—62no—
24C22×#157—22no—
25C2×C32×Q8C2×C411yescharacteristic
26C2×C4×C3⋊D3D411yescharacteristic
27C2×C4×C3⋊D3D411yescharacteristic
28C2×C4×C3⋊D3C2311yescharacteristic
29C2×#634—21no—
30C2×#634C2×C411yescharacteristic
31C2×#622—22no—
32C4⋊#157—24no—
33C4×#157—42no—
34C32×C4⋊C4—21no—
35C32×C4⋊C4C2×C411yescharacteristic
36C32×C42—21no—
37C32×C42C2×C411yescharacteristic
38#3752—21no—
39#3752—21no—
40C4⋊(C3⋊Dic3)—21no—
41C4⋊(C3⋊Dic3)C2×C411yescharacteristic
42#3750—21no—
43#3750—21no—
44#3750—21no—
45#3750—21no—
46#3750—21no—
47C4×C3⋊Dic3—21no—
48C4×C3⋊Dic3C2×C411yescharacteristic
49C4×C3⋊Dic3D411yescharacteristic
50C4×C3⋊Dic3D411yescharacteristic
51#1503—91nomaximal, Sylow
52C3×C4×Q8—22no—
53#946—62no—
54#944—62no—
55#897—62no—
56#896—64no—
57#889—64no—
58#888—62no—
59#872—64no—
60C42×D3—62no—
61C4×Dic6—62no—
62C4×Dic6—64no—
63C22×C3⋊D3C2×D411yescharacteristic
64C2×#157—24no—
65C2×#157—42no—
66C2×#157—42no—
67C32×Q8—41no—
68C2×C32×C4—21no—
69C2×C32×C4—21no—
70C2×C32×C4C22⋊C411yescharacteristic
71C2×C32×C4C22⋊C411yescharacteristic
72C2×C32×C4C22×C411yescharacteristic
73C2×C3⋊Dic3—21no—
74C2×C3⋊Dic3—21no—
75C2×C3⋊Dic3C22⋊C411yescharacteristic
76C2×C3⋊Dic3C22⋊C411yescharacteristic
77C2×C3⋊Dic3C2×D411yescharacteristic
78C4×C3⋊D3—22no—
79C4×C3⋊D3—41no—
80C4×C3⋊D3SD1612yes—
81C4×C3⋊D3Q1612yes—
82#634—42no—
83#634—41no—
84#622—42no—
85#533—91no—
86#431—91no—
87C4×C4⋊C4—91no—
88#328—92no—
89#328—92no—
90C2×C3×Q8—22no—
91C2×C4×D3—62no—
92C2×C4×D3—62no—
93C2×C4×D3—62no—
94C2×Dic6—62no—
95C2×Dic6—64no—
96C3×C4⋊C4—24no—
97C3×C4⋊C4—22no—
98C3×C42—24no—
99C3×C42—22no—
100(C2×D3)⋊C4—64no—
101(C2×D3)⋊C4—64no—
102C4⋊Dic3—62no—
103C4⋊Dic3—64no—
104Dic3⋊C4—64no—
105Dic3⋊C4—64no—
106Dic3⋊C4—64no—
107Dic3⋊C4—64no—
108Dic3⋊C4—64no—
109C4×Dic3—62no—
110C4×Dic3—62no—
111C4×Dic3—62no—
112C4×Dic3—64no—
113C22×C32C2×C22⋊C411yescharacteristic
114C2×C3⋊D3—21no—
115C2×C3⋊D3—21no—
116C2×C3⋊D3C2×SD1611yescharacteristic
117C2×C3⋊D3C2×Q1611yescharacteristic
118#157—44no—
119C32×C4—21no—
120C32×C4—21no—
121C32×C4—41no—
122C32×C4—41no—
123C32×C4#10312yes—
124C3⋊Dic3—21no—
125C3⋊Dic3—41no—
126C3⋊Dic3—41no—
127C3⋊Dic3#10312yes—
128C3⋊Dic3#10412yes—
129C4⋊Q8—91no—
130C4⋊Q8—91no—
131#125—181no—
132C22⋊Q8—91no—
133C22⋊Q8—91no—
134C22⋊Q8—181no—
135C4×Q8—91no—
136C4×Q8—181no—
137C4×Q8#15711yescharacteristic, complemented
138#117—181no—
139C2×C4⋊C4—181no—
140C2×C42—91no—
141C2×C42—181no—
142C4⋊C8—181no—
143C22⋊C8—92no—
144C4×C8—181no—
145#95—92no—
146C22×D3—62no—
147C3×Q8—44no—
148C2×C3×C4—24no—
149C2×C3×C4—24no—
150C2×C3×C4—22no—
151C2×C3×C4—22no—
152C2×C3×C4—22no—
153C2×Dic3—62no—
154C2×Dic3—62no—
155C2×Dic3—62no—
156C2×Dic3—64no—
157C2×Dic3—64no—
158C4×D3—64no—
159C4×D3—64no—
160C4×D3—124no—
161C4×D3—124no—
162Dic6—128no—
163Dic6—124no—
164C2×C32#41011yescharacteristic
165C2×C32C2×#10311yescharacteristic
166C2×C32C2×#10411yescharacteristic
167C3⋊D3—21no—
168C3⋊D3—21no—
169C2×Q8—91no—
170C2×Q8—181no—
171C2×Q8C2×#15711yescharacteristic
172C22×C4—91no—
173C22×C4—91no—
174C22×C4—91no—
175C22×C4—182no—
176C2×C8—182no—
177C4⋊C4—21no—
178C4⋊C4—91no—
179C4⋊C4—181no—
180C4⋊C4—181no—
181C4⋊C4—181no—
182C4⋊C4—181no—
183C4⋊C4—181no—
184C4⋊C4—184no—
185C4⋊C4—181no—
186C4⋊C4C2×#15711yescharacteristic
187C22⋊C4—181no—
188C22⋊C4—181no—
189C42—21no—
190C42—91no—
191C42—91no—
192C42—91no—
193C42—181no—
194C42—362no—
195C42C2×#15711yescharacteristic
196C22×C3—22no—
197C2×D3—62no—
198C2×D3—62no—
199C2×D3—122no—
200C2×D3—122no—
201C3×C4—24no—
202C3×C4—24no—
203C3×C4—42no—
204C3×C4—44no—
205C3×C4—44no—
206Dic3—64no—
207Dic3—64no—
208Dic3—122no—
209Dic3—124no—
210Dic3—124no—
211C32#150311yescharacteristic, complemented, Sylow
212C23—91no—
213Q8—41no—
214Q8—361no—
215Q8—362no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—91no—
219C2×C4—91no—
220C2×C4—92no—
221C2×C4—92no—
222C2×C4—91no—
223C2×C4—182no—
224C2×C4—184no—
225C2×C4—181no—
226C2×C4—181no—
227C2×C4—361no—
228C2×C4—362no—
229C2×C4—362no—
230C2×C4C22⋊#15711yescharacteristic
231C2×C4C22⋊#15711yescharacteristic
232C2×C4C22×#15711yescharacteristic
233C8—362no—
234C2×C3—22no—
235C2×C3—22no—
236C2×C3—22no—
237D3—122no—
238D3—122no—
239C22—91no—
240C22—91no—
241C22—181no—
242C22—181no—
243C22C2×C22⋊#15711yescharacteristic
244C4—21no—
245C4—21no—
246C4—41no—
247C4—41no—
248C4—92no—
249C4—92no—
250C4—181no—
251C4—364no—
252C4—361no—
253C4—361no—
254C4#6378412yes—
255C3—22no—
256C2—181no—
257C2—181no—
258C2#1059379211yescharacteristic
259C2C2×#6378411yescharacteristic
260C2#1059383911yescharacteristic
subgroupG/H
centerC2×C4C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×C4×Q8C4
socleC22×C32C2×C22⋊C4
prime radicalC22×C3⋊D3C2×D4
cosocleC2×C4×C3⋊D3C23
hypercenterC4×Q8#157
hypocenterC32#1503
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
8. C32×C4×Q8C4semidirect
10. #64153C4semidirect
14. #64097C4semidirect
18. C4×#634C4semidirect
137. C4×Q8#157semidirect
211. C32#1503semidirect

Maximal subgroups

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

subgroupindex
#105960492
C4×C4⋊#1572
#105937252
#105902152
#105901582
#15039