Finite Group Databasebeta

← #11775575

Subgroups — #11775575

Order 1152.

766 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 766 conjugacy classes of subgroups — too many to draw. Only its 70 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#10593812C211yesmaximal, characteristic, complemented
3#10593800C211yesmaximal, characteristic, complemented
4#10590209C214yesmaximal, complemented
5C22×C32×D4C411yescharacteristic, complemented
6C22×#638—21no—
7C22×C4×C3⋊D3C2211yescharacteristic
8C2×C22⋊#157—21no—
9C2×C4⋊#157—21no—
10C2×#3787—21no—
11C2×#3757—21no—
12#64147—21no—
13#64147—21no—
14#64147C412yescomplemented
15#64147C2212yes—
16C2×C4⋊(C3⋊Dic3)C411yescharacteristic, complemented
17C22⋊#622—21no—
18#63781C2212yescomplemented
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—42no—
31C2×#638—42no—
32C22×C3⋊Dic3—21no—
33C22×C3⋊Dic3D411yescharacteristic
34C2×C4×C3⋊D3—42no—
35C2×C4×C3⋊D3C2×C411yescharacteristic
36C2×C4×C3⋊D3D411yescharacteristic
37C2×C4×C3⋊D3D411yescharacteristic
38C2×C4×C3⋊D3C2311yescharacteristic
39C22⋊#157—42no—
40C2×#622—22no—
41C4⋊#157—42no—
42#3787—42no—
43#3757—22no—
44#3757—22no—
45C4⋊(C3⋊Dic3)—21no—
46C4⋊(C3⋊Dic3)C2×C412yes—
47#1519—91nomaximal, Sylow
48C22×C3×D4—22no—
49C22×#67—64no—
50C22×C4×D3—62no—
51C2×#217—64no—
52#938—64no—
53#938—64no—
54#938—64no—
55#938—64no—
56C2×C4⋊Dic3—62no—
57C23×C32—22no—
58C23×C32—42no—
59C23×C32—42no—
60C23×C32—42no—
61C23×C32C22⋊C411yescharacteristic
62C22×C3⋊D3—41no—
63C22×C3⋊D3—41no—
64C22×C3⋊D3C22⋊C411yescharacteristic
65C22×C3⋊D3D812yes—
66C22×C3⋊D3SD1612yes—
67C22×C3⋊D3C2×D411yescharacteristic
68C2×#157—42no—
69C2×#157—42no—
70C2×#157—42no—
71C32×D4—42no—
72C32×D4—42no—
73C2×C32×C4—22no—
74C2×C32×C4C22⋊C411yescharacteristic
75C2×C32×C4C22×C411yescharacteristic
76#638—44no—
77#638—42no—
78#638—42no—
79C2×C3⋊Dic3—22no—
80C2×C3⋊Dic3—41no—
81C2×C3⋊Dic3—42no—
82C2×C3⋊Dic3C22⋊C411yescharacteristic
83C2×C3⋊Dic3C2×D411yescharacteristic
84C4×C3⋊D3—22no—
85C4×C3⋊D3—22no—
86C4×C3⋊D3—41no—
87C4×C3⋊D3—41no—
88#622—42no—
89C2×#121—91no—
90C2×C22⋊C8—91no—
91#380—91no—
92#327—94no—
93C24×C3—24no—
94C23×D3—62no—
95C2×C3×D4—24no—
96C2×C3×D4—24no—
97C2×C3×D4—48no—
98C22×C3×C4—22no—
99C2×#67—68no—
100C2×#67—68no—
101C2×#67—128no—
102C2×#67—128no—
103C22×Dic3—62no—
104C22×Dic3—64no—
105C2×C4×D3—62no—
106C2×C4×D3—62no—
107C2×C4×D3—62no—
108C2×C4×D3—62no—
109C2×C4×D3—128no—
110#217—68no—
111#217—68no—
112C4⋊Dic3—64no—
113C4⋊Dic3—64no—
114C22×C32—21no—
115C22×C32—21no—
116C22×C32—42no—
117C22×C32—42no—
118C22×C32—42no—
119C22×C32—84no—
120C22×C32#10212yes—
121C22×C32C2×C22⋊C411yescharacteristic
122C2×C3⋊D3—21no—
123C2×C3⋊D3—21no—
124C2×C3⋊D3—21no—
125C2×C3⋊D3—21no—
126C2×C3⋊D3—42no—
127C2×C3⋊D3—42no—
128C2×C3⋊D3#10212yes—
129C2×C3⋊D3C2×D811yescharacteristic
130C2×C3⋊D3C2×SD1611yescharacteristic
131#157—82no—
132C32×C4—21no—
133C32×C4#9912yes—
134C3⋊Dic3—21no—
135C3⋊Dic3—21no—
136C3⋊Dic3—42no—
137C22×D4—181no—
138C22×D4#15711yescharacteristic, complemented
139C23×C4—91no—
140C22×C8—181no—
141#121—92no—
142#121—92no—
143#121—181no—
144#121—181no—
145C2×C4⋊C4—91no—
146C2×C4⋊C4—181no—
147C2×C22⋊C4—181no—
148C2×C22⋊C4—181no—
149C22⋊C8—92no—
150C22⋊C8—181no—
151#95—92no—
152C23×C3—28no—
153C23×C3—22no—
154C23×C3—48no—
155C23×C3—48no—
156C23×C3—48no—
157C22×D3—62no—
158C22×D3—64no—
159C22×D3—64no—
160C22×D3—62no—
161C22×D3—124no—
162C22×D3—124no—
163C3×D4—48no—
164C3×D4—48no—
165C2×C3×C4—28no—
166C2×C3×C4—22no—
167C2×C3×C4—22no—
168#67—1216no—
169#67—128no—
170#67—128no—
171C2×Dic3—62no—
172C2×Dic3—62no—
173C2×Dic3—68no—
174C2×Dic3—124no—
175C2×Dic3—128no—
176C4×D3—124no—
177C4×D3—124no—
178C4×D3—124no—
179C4×D3—124no—
180C2×C32—22no—
181C2×C32—82no—
182C2×C32C2×#9911yescharacteristic
183C2×C32C2×#10211yescharacteristic
184C2×C32#42111yescharacteristic
185C3⋊D3—21no—
186C3⋊D3—22no—
187C3⋊D3—21no—
188C24—21no—
189C24—91no—
190C2×D4—21no—
191C2×D4—42no—
192C2×D4—182no—
193C2×D4—182no—
194C2×D4—362no—
195C2×D4—362no—
196C2×D4C2×#15712yes—
197C22×C4—91no—
198C22×C4—91no—
199C22×C4—91no—
200C22×C4—91no—
201C22×C4—91no—
202C22×C4—181no—
203C22×C4—182no—
204C22×C4—362no—
205C22×C4C2×#15711yescharacteristic
206C2×C8—182no—
207C2×C8—362no—
208C4⋊C4—92no—
209C4⋊C4—181no—
210C4⋊C4—362no—
211C22⋊C4—182no—
212C22⋊C4—182no—
213C22⋊C4—362no—
214C22×C3—24no—
215C22×C3—24no—
216C22×C3—22no—
217C22×C3—24no—
218C22×C3—48no—
219C22×C3—48no—
220C22×C3—48no—
221C22×C3—816no—
222C2×D3—64no—
223C2×D3—62no—
224C2×D3—62no—
225C2×D3—122no—
226C2×D3—122no—
227C2×D3—122no—
228C2×D3—122no—
229C2×D3—128no—
230C2×D3—128no—
231C3×C4—24no—
232C3×C4—24no—
233Dic3—122no—
234Dic3—122no—
235Dic3—128no—
236C32#151911yescharacteristic, complemented, Sylow
237C23—22no—
238C23—42no—
239C23—42no—
240C23—42no—
241C23—91no—
242C23—91no—
243C23—92no—
244C23—92no—
245C23—361no—
246C23—361no—
247C23C22⋊#15711yescharacteristic
248D4—42no—
249D4—42no—
250D4—362no—
251D4—362no—
252D4—364no—
253C2×C4—22no—
254C2×C4—91no—
255C2×C4—91no—
256C2×C4—182no—
257C2×C4—182no—
258C2×C4—182no—
259C2×C4—361no—
260C2×C4—361no—
261C2×C4—361no—
262C2×C4—362no—
263C2×C4—362no—
264C2×C4—362no—
265C2×C4—362no—
266C2×C4C22⋊#15711yescharacteristic
267C2×C4C22×#15711yescharacteristic
268C8—362no—
269C2×C3—28no—
270C2×C3—22no—
271C2×C3—22no—
272C2×C3—22no—
273C2×C3—88no—
274D3—122no—
275D3—124no—
276D3—122no—
277C22—21no—
278C22—21no—
279C22—42no—
280C22—42no—
281C22—42no—
282C22—84no—
283C22—91no—
284C22—91no—
285C22—92no—
286C22—181no—
287C22—181no—
288C22—181no—
289C22—181no—
290C22—362no—
291C22—362no—
292C22#6378212yes—
293C22C2×C22⋊#15711yescharacteristic
294C4—21no—
295C4—181no—
296C4—181no—
297C4—362no—
298C4—722no—
299C4#6378612yes—
300C3—22no—
301C2—22no—
302C2—82no—
303C2—181no—
304C2—181no—
305C2—182no—
306C2C2×#6378211yescharacteristic
307C2#1059381611yescharacteristic
308C2C2×#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#1519
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. #10593812C2semidirect
3. #10593800C2semidirect
4. #10590209C2semidirect
5. C22×C32×D4C4semidirect
14. #64147C4semidirect
16. C2×C4⋊(C3⋊Dic3)C4semidirect
18. #63781C22semidirect
19. #63778C22semidirect
138. C22×D4#157semidirect
236. C32#1519semidirect

Maximal subgroups

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

subgroupindex
C2×#641472
#105938122
#105938002
#105902092
#15199