Finite Group Databasebeta

← #11775297

Subgroups — #11775297

Order 1152.

752 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 752 conjugacy classes of subgroups — too many to draw. Only its 60 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×#64104C211yesmaximal, characteristic
2#10593811C211yesmaximal, characteristic, complemented
3#10593802C211yesmaximal, characteristic, complemented
4#10590157C214yesmaximal, complemented
5C22×C4⋊(C3⋊D3)—21no—
6C22×C4⋊(C3⋊D3)C411yescharacteristic, complemented
7C22×C4×C3⋊D3C2211yescharacteristic
8C2×C22⋊#157—21no—
9C2×#3792—21no—
10C2×C32×C4⋊C4C411yescharacteristic, complemented
11C2×#3752—21no—
12#64104—21no—
13#64104—21no—
14#64104C412yescomplemented
15#64104C2212yes—
16#63781—21no—
17#63781C2212yescomplemented
18#63778—21no—
19#63778C2212yescomplemented
20C2×#895—62no—
21C23×C3⋊D3—21no—
22C23×C3⋊D3D411yescharacteristic
23C22×#157—22no—
24C22×C32×C4—21no—
25C22×C32×C4C2×C411yescharacteristic
26C22×C3⋊Dic3D411yescharacteristic
27C2×C4⋊(C3⋊D3)—22no—
28C2×C4⋊(C3⋊D3)—22no—
29C2×C4⋊(C3⋊D3)—21no—
30C2×C4⋊(C3⋊D3)—42no—
31C2×C4⋊(C3⋊D3)—44no—
32C2×C4⋊(C3⋊D3)C2×C412yes—
33C2×C4×C3⋊D3—42no—
34C2×C4×C3⋊D3C2×C411yescharacteristic
35C2×C4×C3⋊D3D411yescharacteristic
36C2×C4×C3⋊D3D411yescharacteristic
37C2×C4×C3⋊D3C2311yescharacteristic
38C22⋊#157—42no—
39#3792—42no—
40C2×#622—22no—
41C32×C4⋊C4—21no—
42C32×C4⋊C4C2×C412yes—
43#3752—22no—
44#3752—22no—
45#1510—91nomaximal, Sylow
46C22×D12—62no—
47C22×D12—64no—
48C22×C4×D3—62no—
49C2×C3×C4⋊C4—22no—
50C2×(C2×D3)⋊C4—64no—
51#895—64no—
52#895—64no—
53#895—64no—
54#895—64no—
55C23×C32C22⋊C411yescharacteristic
56C22×C3⋊D3—22no—
57C22×C3⋊D3—22no—
58C22×C3⋊D3—22no—
59C22×C3⋊D3—41no—
60C22×C3⋊D3—42no—
61C22×C3⋊D3—42no—
62C22×C3⋊D3—42no—
63C22×C3⋊D3C22⋊C411yescharacteristic
64C22×C3⋊D3C2×D411yescharacteristic
65C2×#157—42no—
66C2×#157—42no—
67C2×#157—42no—
68C2×C32×C4—22no—
69C2×C32×C4—22no—
70C2×C32×C4—42no—
71C2×C32×C4C22⋊C411yescharacteristic
72C2×C32×C4C22×C411yescharacteristic
73C2×C3⋊Dic3—22no—
74C2×C3⋊Dic3C22⋊C411yescharacteristic
75C2×C3⋊Dic3C2×D411yescharacteristic
76C4⋊(C3⋊D3)—42no—
77C4⋊(C3⋊D3)—42no—
78C4⋊(C3⋊D3)—44no—
79C4⋊(C3⋊D3)—44no—
80C4×C3⋊D3—41no—
81C4×C3⋊D3—41no—
82C4×C3⋊D3—41no—
83C4×C3⋊D3—41no—
84#622—42no—
85C2×#121—91no—
86#407—91no—
87#381—91no—
88#327—94no—
89C23×D3—62no—
90C23×D3—64no—
91C22×C3×C4—24no—
92C22×C3×C4—22no—
93C22×Dic3—62no—
94C2×D12—64no—
95C2×D12—68no—
96C2×D12—68no—
97C2×D12—64no—
98C2×D12—128no—
99C2×D12—1216no—
100C2×C4×D3—62no—
101C2×C4×D3—62no—
102C2×C4×D3—62no—
103C2×C4×D3—62no—
104C2×C4×D3—128no—
105C3×C4⋊C4—24no—
106C3×C4⋊C4—24no—
107(C2×D3)⋊C4—68no—
108(C2×D3)⋊C4—68no—
109C22×C32—21no—
110C22×C32—21no—
111C22×C32#9912yes—
112C22×C32C2×C22⋊C411yescharacteristic
113C2×C3⋊D3—21no—
114C2×C3⋊D3—21no—
115C2×C3⋊D3—21no—
116C2×C3⋊D3—21no—
117C2×C3⋊D3—21no—
118C2×C3⋊D3—44no—
119C2×C3⋊D3—42no—
120C2×C3⋊D3—42no—
121C2×C3⋊D3—42no—
122C2×C3⋊D3—84no—
123C2×C3⋊D3AGL(1,ℤ/8)12yes—
124#157—82no—
125C32×C4—21no—
126C32×C4—21no—
127C32×C4—42no—
128C3⋊Dic3—21no—
129C3⋊Dic3—21no—
130C22×D4—91no—
131C22×D4—181no—
132C23×C4—91no—
133C2×M16—181no—
134#121—92no—
135#121—92no—
136#121—181no—
137#121—181no—
138C2×C4⋊C4#15711yescharacteristic, complemented
139C2×C22⋊C4—181no—
140C2×C22⋊C4—181no—
141C22⋊C8—92no—
142C22⋊C8—181no—
143#95—92no—
144#95—181no—
145C23×C3—22no—
146C22×D3—62no—
147C22×D3—62no—
148C22×D3—68no—
149C22×D3—68no—
150C22×D3—124no—
151C22×D3—124no—
152C22×D3—128no—
153C22×D3—128no—
154C22×D3—128no—
155C2×C3×C4—28no—
156C2×C3×C4—28no—
157C2×C3×C4—22no—
158C2×C3×C4—22no—
159C2×C3×C4—48no—
160C2×Dic3—62no—
161C2×Dic3—62no—
162C2×Dic3—124no—
163D12—128no—
164D12—128no—
165D12—1216no—
166D12—1216no—
167C4×D3—124no—
168C4×D3—124no—
169C4×D3—124no—
170C4×D3—124no—
171C2×C32—22no—
172C2×C32C2×#9911yescharacteristic
173C2×C32#41811yescharacteristic
174C2×C32#42111yescharacteristic
175C3⋊D3—22no—
176C3⋊D3—41no—
177C3⋊D3—82no—
178C24—91no—
179C24—181no—
180C2×D4—92no—
181C2×D4—182no—
182C2×D4—182no—
183C2×D4—181no—
184C2×D4—362no—
185C2×D4—364no—
186C22×C4—21no—
187C22×C4—91no—
188C22×C4—91no—
189C22×C4—91no—
190C22×C4—91no—
191C22×C4—91no—
192C22×C4—182no—
193C22×C4—362no—
194C22×C4C2×#15711yescharacteristic
195M16—362no—
196C2×C8—182no—
197C4⋊C4—21no—
198C4⋊C4C2×#15712yes—
199C22⋊C4—182no—
200C22⋊C4—182no—
201C22⋊C4—362no—
202C22×C3—24no—
203C22×C3—24no—
204C22×C3—24no—
205C22×C3—22no—
206C2×D3—64no—
207C2×D3—64no—
208C2×D3—122no—
209C2×D3—122no—
210C2×D3—122no—
211C2×D3—122no—
212C2×D3—1216no—
213C2×D3—128no—
214C2×D3—128no—
215C2×D3—128no—
216C2×D3—2416no—
217C3×C4—24no—
218C3×C4—24no—
219C3×C4—48no—
220Dic3—122no—
221Dic3—122no—
222C32#151011yescharacteristic, complemented, Sylow
223C23—91no—
224C23—91no—
225C23—182no—
226C23—182no—
227C23—182no—
228C23—361no—
229C23—362no—
230C23—362no—
231C23—362no—
232C23C22⋊#15711yescharacteristic
233D4—362no—
234D4—362no—
235D4—364no—
236D4—364no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—42no—
240C2×C4—91no—
241C2×C4—91no—
242C2×C4—182no—
243C2×C4—361no—
244C2×C4—361no—
245C2×C4—361no—
246C2×C4—361no—
247C2×C4—362no—
248C2×C4—362no—
249C2×C4—362no—
250C2×C4C22⋊#15711yescharacteristic
251C2×C4C22×#15711yescharacteristic
252C8—362no—
253C2×C3—28no—
254C2×C3—22no—
255C2×C3—22no—
256C2×C3—22no—
257D3—124no—
258D3—124no—
259D3—248no—
260C22—21no—
261C22—21no—
262C22—92no—
263C22—181no—
264C22—181no—
265C22—181no—
266C22—181no—
267C22—181no—
268C22—364no—
269C22—362no—
270C22—362no—
271C22—362no—
272C22—724no—
273C22#6377412yes—
274C22C2×C22⋊#15711yescharacteristic
275C4—21no—
276C4—21no—
277C4—42no—
278C4—181no—
279C4—181no—
280C4—722no—
281C3—22no—
282C2—22no—
283C2—182no—
284C2—361no—
285C2—722no—
286C2C2×#6377411yescharacteristic
287C2#1059381411yescharacteristic
288C2#1059383111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC2×C32×C4⋊C4C4
socleC22×C32C2×C22⋊C4
prime radicalC2×#64104C2
cosocleC2×C4×C3⋊D3C23
hypercenterC2×C4⋊C4#157
hypocenterC32#1510
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #10593811C2semidirect
3. #10593802C2semidirect
4. #10590157C2semidirect
6. C22×C4⋊(C3⋊D3)C4semidirect
10. C2×C32×C4⋊C4C4semidirect
14. #64104C4semidirect
17. #63781C22semidirect
19. #63778C22semidirect
138. C2×C4⋊C4#157semidirect
222. C32#1510semidirect

Maximal subgroups

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

subgroupindex
C2×#641042
#105938112
#105938022
#105901572
#15109