Finite Group Databasebeta

← #11775358

Subgroups — #11775358

Order 1152.

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

normal subgroups only

This group has 456 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#10596162C211yesmaximal, characteristic
2#10593736C211yesmaximal, characteristic, complemented
3#10593730C211yesmaximal, characteristic, complemented
4#10590158C212yesmaximal, complemented
5#10590157C212yesmaximal
6C2×C4⋊#157—21no—
7C32×#125C411yescharacteristic, complemented
8#64107—21no—
9#64106C2211yescharacteristic
10#64104C2211yescharacteristic
11#64103—21no—
12#64102—21no—
13#64102C411yescharacteristic, complemented
14#64101—21no—
15#64096C411yescharacteristic, complemented
16#64084C411yescharacteristic, complemented
17C42×C3⋊D3C2211yescharacteristic
18#63781—21no—
19#63781C2212yes—
20#63778C2212yes—
21#63777—21no—
22C4⋊#622—21no—
23#5691—62no—
24C22×#157—22no—
25C2×C4⋊(C3⋊D3)—21no—
26C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
27C2×C4×C3⋊D3—21no—
28C2×C4×C3⋊D3D411yescharacteristic
29C2×C4×C3⋊D3D411yescharacteristic
30C2×C4×C3⋊D3C2311yescharacteristic
31C2×#634C2×C411yescharacteristic
32C2×#622—22no—
33C4⋊#157—42no—
34C32×C4⋊C4—21no—
35C32×C4⋊C4—21no—
36C32×C4⋊C4C2×C411yescharacteristic
37C32×C4⋊C4C2×C411yescharacteristic
38C32×C42C2×C411yescharacteristic
39#3752—21no—
40#3752—21no—
41#3752—21no—
42#3752—21no—
43#3752—21no—
44C4⋊(C3⋊Dic3)—21no—
45#3750—21no—
46C4×C3⋊Dic3—21no—
47C4×C3⋊Dic3C2×C411yescharacteristic
48C4×C3⋊Dic3D411yescharacteristic
49C4×C3⋊Dic3D411yescharacteristic
50#1512—91nomaximal, Sylow
51C3×#125—22no—
52#898—64no—
53#897—62no—
54#895—62no—
55#894—64no—
56#893—62no—
57#893—64no—
58#892—64no—
59#887—62no—
60#875—62no—
61C42×D3—62no—
62C22×C3⋊D3—21no—
63C22×C3⋊D3C2×D411yescharacteristic
64C2×#157—42no—
65C2×#157—42no—
66C2×#157—42no—
67C2×C32×C4—21no—
68C2×C32×C4—21no—
69C2×C32×C4C22⋊C411yescharacteristic
70C2×C32×C4C22⋊C411yescharacteristic
71C2×C32×C4C22×C411yescharacteristic
72C2×C3⋊Dic3—21no—
73C2×C3⋊Dic3C22⋊C411yescharacteristic
74C2×C3⋊Dic3C22⋊C411yescharacteristic
75C2×C3⋊Dic3C2×D411yescharacteristic
76C4⋊(C3⋊D3)—41no—
77C4⋊(C3⋊D3)—41no—
78C4⋊(C3⋊D3)—41no—
79C4×C3⋊D3—21no—
80C4×C3⋊D3—21no—
81C4×C3⋊D3—41no—
82C4×C3⋊D3—41no—
83C4×C3⋊D3—42no—
84#634—41no—
85#622—42no—
86#529—91no—
87#432—91no—
88#382—91no—
89#328—92no—
90#327—92no—
91C2×D12—62no—
92C2×D12—64no—
93C2×C4×D3—62no—
94C2×C4×D3—62no—
95C2×C4×D3—62no—
96C2×C4×D3—64no—
97C2×Dic6—62no—
98C3×C4⋊C4—24no—
99C3×C4⋊C4—24no—
100C3×C4⋊C4—22no—
101C3×C4⋊C4—22no—
102C3×C42—22no—
103(C2×D3)⋊C4—64no—
104(C2×D3)⋊C4—64no—
105(C2×D3)⋊C4—64no—
106(C2×D3)⋊C4—64no—
107(C2×D3)⋊C4—64no—
108C4⋊Dic3—64no—
109Dic3⋊C4—64no—
110C4×Dic3—62no—
111C4×Dic3—62no—
112C4×Dic3—62no—
113C4×Dic3—64no—
114C22×C32C2×C22⋊C411yescharacteristic
115C2×C3⋊D3—21no—
116C2×C3⋊D3—21no—
117C2×C3⋊D3—41no—
118C2×C3⋊D3—41no—
119C2×C3⋊D3—41no—
120C2×C3⋊D3AGL(1,ℤ/8)11yescharacteristic
121C2×C3⋊D3#13711yescharacteristic
122#157—82no—
123C32×C4—21no—
124C32×C4—21no—
125C32×C4—21no—
126C32×C4—41no—
127C32×C4—41no—
128C3⋊Dic3—21no—
129C3⋊Dic3—21no—
130C3⋊Dic3—21no—
131C3⋊Dic3—41no—
132#126—181no—
133#125#15711yescharacteristic, complemented
134#124—91no—
135#123—181no—
136C22⋊Q8—91no—
137#121—91no—
138C4×Q8—91no—
139C4×D4—91no—
140C4×D4—181no—
141#117—181no—
142C2×C4⋊C4—181no—
143C2×C42—91no—
144C4⋊C8—181no—
145C22⋊C8—92no—
146#97—181no—
147#95—92no—
148#95—181no—
149C22×D3—62no—
150C22×D3—64no—
151C2×C3×C4—24no—
152C2×C3×C4—24no—
153C2×C3×C4—22no—
154C2×C3×C4—22no—
155C2×C3×C4—22no—
156C2×Dic3—62no—
157C2×Dic3—62no—
158C2×Dic3—62no—
159C2×Dic3—64no—
160D12—124no—
161D12—124no—
162D12—124no—
163C4×D3—122no—
164C4×D3—122no—
165C4×D3—124no—
166C4×D3—128no—
167C4×D3—124no—
168Dic6—124no—
169C2×C32#41011yescharacteristic
170C2×C32#41711yescharacteristic
171C2×C32#42111yescharacteristic
172C3⋊D3—21no—
173C3⋊D3—21no—
174C3⋊D3—81no—
175C2×Q8—91no—
176C2×D4—91no—
177C2×D4—181no—
178C22×C4—91no—
179C22×C4—91no—
180C22×C4—91no—
181C22×C4—181no—
182C22×C4—182no—
183C2×C8—182no—
184C4⋊C4—21no—
185C4⋊C4—21no—
186C4⋊C4—181no—
187C4⋊C4—181no—
188C4⋊C4—362no—
189C4⋊C4C2×#15711yescharacteristic
190C4⋊C4C2×#15711yescharacteristic
191C22⋊C4—181no—
192C22⋊C4—181no—
193C22⋊C4—181no—
194C22⋊C4—181no—
195C22⋊C4—181no—
196C42—91no—
197C42—91no—
198C42—91no—
199C42—181no—
200C42C2×#15711yescharacteristic
201C22×C3—22no—
202C2×D3—62no—
203C2×D3—62no—
204C2×D3—122no—
205C2×D3—122no—
206C2×D3—124no—
207C2×D3—124no—
208C2×D3—124no—
209C3×C4—24no—
210C3×C4—42no—
211C3×C4—42no—
212C3×C4—44no—
213C3×C4—44no—
214Dic3—64no—
215Dic3—122no—
216Dic3—122no—
217Dic3—124no—
218C32#151211yescharacteristic, complemented, Sylow
219C23—91no—
220C23—181no—
221Q8—361no—
222D4—361no—
223D4—361no—
224D4—361no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—91no—
228C2×C4—91no—
229C2×C4—91no—
230C2×C4—181no—
231C2×C4—181no—
232C2×C4—181no—
233C2×C4—361no—
234C2×C4—361no—
235C2×C4—362no—
236C2×C4—362no—
237C2×C4—362no—
238C2×C4—362no—
239C2×C4C22⋊#15711yescharacteristic
240C2×C4C22⋊#15711yescharacteristic
241C2×C4C22×#15711yescharacteristic
242C8—362no—
243C2×C3—22no—
244C2×C3—22no—
245C2×C3—22no—
246D3—122no—
247D3—122no—
248D3—244no—
249C22—91no—
250C22—91no—
251C22—181no—
252C22—181no—
253C22—361no—
254C22—361no—
255C22—361no—
256C22C2×C22⋊#15711yescharacteristic
257C4—21no—
258C4—21no—
259C4—21no—
260C4—41no—
261C4—41no—
262C4—181no—
263C4—181no—
264C4—181no—
265C4—361no—
266C4—722no—
267C3—22no—
268C2—181no—
269C2—181no—
270C2—721no—
271C2#1059383211yescharacteristic
272C2#1059384011yescharacteristic
273C2#1059384211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×#125C4
socleC22×C32C2×C22⋊C4
prime radical#64104C22
cosocleC2×C4×C3⋊D3C23
hypercenter#125#157
hypocenterC32#1512
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
2. #10593736C2semidirect
3. #10593730C2semidirect
4. #10590158C2semidirect
7. C32×#125C4semidirect
13. #64102C4semidirect
15. #64096C4semidirect
16. #64084C4semidirect
133. #125#157semidirect
218. C32#1512semidirect

Maximal subgroups

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

subgroupindex
#105961622
#105937362
#105937302
#105901582
#105901572
#15129