Finite Group Databasebeta

← #11775296

Subgroups — #11775296

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×#64147C211yesmaximal, characteristic
2#10593811C211yesmaximal, characteristic, complemented
3#10593802C211yesmaximal, characteristic, complemented
4#10590209C214yesmaximal, complemented
5C22×C32×D4C411yescharacteristic, complemented
6C22×#638—21no—
7C22×C4×C3⋊D3C2211yescharacteristic
8C2×C22⋊#157—21no—
9C2×#3792—21no—
10C2×#3757—21no—
11#64147—21no—
12#64147—21no—
13#64147C412yescomplemented
14#64147C2212yes—
15C2×C4⋊(C3⋊Dic3)C411yescharacteristic, complemented
16#63781—21no—
17#63781C2212yescomplemented
18#63778—21no—
19#63778C2212yescomplemented
20C2×#938—62no—
21C24×C32—21no—
22C23×C3⋊D3D411yescharacteristic
23C22×#157—22no—
24C2×C32×D4—21no—
25C2×C32×D4—42no—
26C2×C32×D4C2×C412yes—
27C22×C32×C4C2×C411yescharacteristic
28C2×#638—22no—
29C2×#638—22no—
30C2×#638—44no—
31C22×C3⋊Dic3—21no—
32C22×C3⋊Dic3D411yescharacteristic
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—
41#3757—22no—
42#3757—22no—
43C4⋊(C3⋊Dic3)—21no—
44C4⋊(C3⋊Dic3)C2×C412yes—
45#1510—91nomaximal, Sylow
46C22×C3×D4—22no—
47C22×#67—64no—
48C22×C4×D3—62no—
49C2×#217—64no—
50#938—64no—
51#938—64no—
52#938—64no—
53#938—64no—
54C2×C4⋊Dic3—62no—
55C23×C32—22no—
56C23×C32—42no—
57C23×C32—42no—
58C23×C32—42no—
59C23×C32C22⋊C411yescharacteristic
60C22×C3⋊D3—22no—
61C22×C3⋊D3—22no—
62C22×C3⋊D3—41no—
63C22×C3⋊D3C22⋊C411yescharacteristic
64C22×C3⋊D3C2×D411yescharacteristic
65C2×#157—42no—
66C2×#157—42no—
67C2×#157—42no—
68C32×D4—42no—
69C32×D4—42no—
70C2×C32×C4—22no—
71C2×C32×C4C22⋊C411yescharacteristic
72C2×C32×C4C22×C411yescharacteristic
73#638—44no—
74#638—44no—
75C2×C3⋊Dic3—22no—
76C2×C3⋊Dic3—22no—
77C2×C3⋊Dic3—42no—
78C2×C3⋊Dic3C22⋊C411yescharacteristic
79C2×C3⋊Dic3C2×D411yescharacteristic
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—
89C24×C3—24no—
90C23×D3—62no—
91C2×C3×D4—24no—
92C2×C3×D4—24no—
93C2×C3×D4—48no—
94C22×C3×C4—22no—
95C2×#67—68no—
96C2×#67—68no—
97C2×#67—1216no—
98C22×Dic3—62no—
99C22×Dic3—64no—
100C2×C4×D3—62no—
101C2×C4×D3—62no—
102C2×C4×D3—62no—
103C2×C4×D3—62no—
104C2×C4×D3—128no—
105#217—68no—
106#217—68no—
107C4⋊Dic3—64no—
108C4⋊Dic3—64no—
109C22×C32—21no—
110C22×C32—21no—
111C22×C32—42no—
112C22×C32—42no—
113C22×C32—42no—
114C22×C32—84no—
115C22×C32#9912yes—
116C22×C32C2×C22⋊C411yescharacteristic
117C2×C3⋊D3—21no—
118C2×C3⋊D3—21no—
119C2×C3⋊D3—21no—
120C2×C3⋊D3—21no—
121C2×C3⋊D3—21no—
122C2×C3⋊D3—44no—
123C2×C3⋊D3AGL(1,ℤ/8)12yes—
124#157—82no—
125C32×C4—21no—
126C32×C4—21no—
127C3⋊Dic3—21no—
128C3⋊Dic3—21no—
129C3⋊Dic3—42no—
130C22×D4—181no—
131C22×D4#15711yescharacteristic, complemented
132C23×C4—91no—
133C2×M16—181no—
134#121—92no—
135#121—92no—
136#121—181no—
137#121—181no—
138C2×C4⋊C4—91no—
139C2×C22⋊C4—181no—
140C2×C22⋊C4—181no—
141C22⋊C8—92no—
142C22⋊C8—181no—
143#95—92no—
144#95—181no—
145C23×C3—28no—
146C23×C3—22no—
147C23×C3—48no—
148C23×C3—48no—
149C23×C3—48no—
150C22×D3—62no—
151C22×D3—62no—
152C22×D3—68no—
153C22×D3—124no—
154C22×D3—124no—
155C3×D4—48no—
156C3×D4—48no—
157C2×C3×C4—28no—
158C2×C3×C4—22no—
159C2×C3×C4—22no—
160#67—1216no—
161#67—1216no—
162C2×Dic3—62no—
163C2×Dic3—62no—
164C2×Dic3—68no—
165C2×Dic3—124no—
166C2×Dic3—128no—
167C4×D3—124no—
168C4×D3—124no—
169C4×D3—124no—
170C4×D3—124no—
171C2×C32—22no—
172C2×C32—82no—
173C2×C32C2×#9911yescharacteristic
174C2×C32#41811yescharacteristic
175C2×C32#42111yescharacteristic
176C3⋊D3—22no—
177C3⋊D3—41no—
178C24—21no—
179C24—91no—
180C2×D4—21no—
181C2×D4—42no—
182C2×D4—182no—
183C2×D4—182no—
184C2×D4—364no—
185C2×D4C2×#15712yes—
186C22×C4—91no—
187C22×C4—91no—
188C22×C4—91no—
189C22×C4—91no—
190C22×C4—91no—
191C22×C4—181no—
192C22×C4—182no—
193C22×C4—362no—
194C22×C4C2×#15711yescharacteristic
195M16—362no—
196C2×C8—182no—
197C4⋊C4—92no—
198C4⋊C4—181no—
199C22⋊C4—182no—
200C22⋊C4—182no—
201C22⋊C4—362no—
202C22×C3—24no—
203C22×C3—24no—
204C22×C3—22no—
205C22×C3—24no—
206C22×C3—48no—
207C22×C3—48no—
208C22×C3—48no—
209C22×C3—816no—
210C2×D3—64no—
211C2×D3—64no—
212C2×D3—122no—
213C2×D3—122no—
214C2×D3—122no—
215C2×D3—122no—
216C2×D3—1216no—
217C3×C4—24no—
218C3×C4—24no—
219Dic3—122no—
220Dic3—122no—
221Dic3—128no—
222C32#151011yescharacteristic, complemented, Sylow
223C23—22no—
224C23—42no—
225C23—42no—
226C23—42no—
227C23—91no—
228C23—91no—
229C23—182no—
230C23—182no—
231C23—361no—
232C23C22⋊#15711yescharacteristic
233D4—42no—
234D4—42no—
235D4—364no—
236D4—364no—
237C2×C4—22no—
238C2×C4—91no—
239C2×C4—91no—
240C2×C4—182no—
241C2×C4—182no—
242C2×C4—361no—
243C2×C4—361no—
244C2×C4—361no—
245C2×C4—361no—
246C2×C4—362no—
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—
257C2×C3—88no—
258D3—124no—
259D3—124no—
260C22—21no—
261C22—21no—
262C22—42no—
263C22—42no—
264C22—42no—
265C22—84no—
266C22—92no—
267C22—181no—
268C22—181no—
269C22—181no—
270C22—181no—
271C22—181no—
272C22—364no—
273C22#6378612yes—
274C22C2×C22⋊#15711yescharacteristic
275C4—21no—
276C4—21no—
277C4—181no—
278C4—181no—
279C4—362no—
280C4—722no—
281C3—22no—
282C2—22no—
283C2—82no—
284C2—182no—
285C2—361no—
286C2#1059381411yescharacteristic
287C2#1059381611yescharacteristic
288C2C2×#6378611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC22×C32×D4C4
socleC22×C32C2×C22⋊C4
prime radicalC2×#64147C2
cosocleC2×C4×C3⋊D3C23
hypercenterC22×D4#157
hypocenterC32#1510
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. #10593811C2semidirect
3. #10593802C2semidirect
4. #10590209C2semidirect
5. C22×C32×D4C4semidirect
13. #64147C4semidirect
15. C2×C4⋊(C3⋊Dic3)C4semidirect
17. #63781C22semidirect
19. #63778C22semidirect
131. C22×D4#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×#641472
#105938112
#105938022
#105902092
#15109