Finite Group Databasebeta

← #11801826

Subgroups — #11801826

Order 1152.

986 conjugacy classes of subgroups; only the 218 normal subgroups are shown.

normal subgroups only

This group has 986 conjugacy classes of subgroups — too many to draw. Only its 218 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×#64286C211yesmaximal, characteristic
2C22×C4×#157C211yesmaximal, characteristic
3C3⋊D3×#117C211yesmaximal, characteristic
4#10593759C214yesmaximal, complemented
5#10593746C214yesmaximal
6C4×C4⋊#157C214yesmaximal, complemented
7C23×#157C2212yes—
8C22×C4×C3⋊D3C2211yescharacteristic
9C2×C22⋊#157C2212yes—
10#64286—24no—
11C2×C4⋊#157C2212yes—
12C2×C4⋊#157C2218yes—
13C2×C4×#157—24no—
14C2×C4×#157C2212yes—
15C2×C4×#157C2212yes—
16C2×C4×#157C2212yes—
17C32×#117C411yescharacteristic, complemented
18#64135C411yescharacteristic, complemented
19#64101C412yescomplemented
20C4⋊C4×C3⋊D3C2212yes—
21C22⋊C4×C3⋊D3C2212yes—
22#64086C412yescomplemented
23#64081C412yescomplemented
24C42×C3⋊D3C2212yes—
25#63781C2218yes—
26D3×#117—62no—
27C23×C3⋊D3C2311yescharacteristic
28C22×#157—24no—
29C22×#157—28no—
30C22×#157C2314yes—
31C22×#157C2314yes—
32C22×C32×C4C2×C411yescharacteristic
33C22×C3⋊Dic3C2×C411yescharacteristic
34C2×C4×C3⋊D3C2×C411yescharacteristic
35C2×C4×C3⋊D3C2×C411yescharacteristic
36C2×C4×C3⋊D3D414yes—
37C2×C4×C3⋊D3Q814yes—
38C2×C4×C3⋊D3C2314yes—
39C2×C4×C3⋊D3C2311yescharacteristic
40C2×C4×C3⋊D3C2311yescharacteristic
41C22⋊#157—24no—
42C4⋊#157—216no—
43C4⋊#157—24no—
44C4×#157—24no—
45C4×#157—24no—
46C4×#157—24no—
47C32×C4⋊C4C2×C412yescomplemented
48C32×C22⋊C4C2×C412yes—
49C32×C42C2×C412yescomplemented
50#3757C2×C412yes—
51#3752C2×C414yes—
52C4⋊(C3⋊Dic3)C2×C412yescomplemented
53#3750C2×C414yescomplemented
54C4×C3⋊Dic3C2×C412yescomplemented
55C4×C3⋊Dic3C2×C414yescomplemented
56#2296—91nomaximal, Sylow
57C22×C4×D3—62no—
58C3×#117—22no—
59#926—62no—
60#892—64no—
61D3×C4⋊C4—64no—
62D3×C22⋊C4—64no—
63#877—64no—
64#872—64no—
65C42×D3—64no—
66C23×C32C22×C411yescharacteristic
67C22×C3⋊D3—24no—
68C22×C3⋊D3C22×C411yescharacteristic
69C22×C3⋊D3C2×D412yes—
70C22×C3⋊D3C2×Q812yes—
71C22×C3⋊D3C2411yescharacteristic
72C2×#157—216no—
73C2×#157—24no—
74C2×#157—24no—
75C2×#157—24no—
76C2×#157—28no—
77C2×#157#4118yes—
78C2×C32×C4C4⋊C414yescomplemented
79C2×C32×C4C22×C414yes—
80C2×C32×C4C22×C411yescharacteristic
81C2×C32×C4C22×C411yescharacteristic
82C2×C3⋊Dic3C4⋊C414yescomplemented
83C2×C3⋊Dic3C22×C414yes—
84C2×C3⋊Dic3C22×C411yescharacteristic
85C2×C3⋊Dic3C22×C411yescharacteristic
86C4×C3⋊D3—28no—
87C4×C3⋊D3C4⋊C414yescomplemented
88C4×C3⋊D3C4⋊C414yescomplemented
89C4×C3⋊D3C2×D412yes—
90C4×C3⋊D3C2×D412yes—
91C4×C3⋊D3C2×Q812yes—
92C4×C3⋊D3C2×Q812yes—
93C2×#117—91no—
94C2×#117—91no—
95C22×C42—91no—
96#389—94no—
97#385—94no—
98C4×C4⋊C4—94no—
99C23×D3—62no—
100C22×C3×C4—22no—
101C22×Dic3—62no—
102C2×C4×D3—62no—
103C2×C4×D3—62no—
104C2×C4×D3—62no—
105C2×C4×D3—62no—
106C2×C4×D3—68no—
107C2×C4×D3—68no—
108C2×C4×D3—68no—
109C3×C4⋊C4—24no—
110C3×C22⋊C4—24no—
111C3×C42—24no—
112#217—64no—
113(C2×D3)⋊C4—68no—
114C4⋊Dic3—64no—
115Dic3⋊C4—68no—
116C4×Dic3—64no—
117C4×Dic3—68no—
118C22×C32—22no—
119C22×C32C2×C4⋊C412yes—
120C22×C32C23×C411yescharacteristic
121C2×C3⋊D3—22no—
122C2×C3⋊D3—24no—
123C2×C3⋊D3—24no—
124C2×C3⋊D3C2×C4⋊C412yes—
125C2×C3⋊D3C22×D411yescharacteristic
126C2×C3⋊D3C22×Q811yescharacteristic
127C2×C3⋊D3C2×#4114yes—
128#157—28no—
129#157—44no—
130C32×C4—24no—
131C32×C4C2×C4⋊C412yes—
132C32×C4C2×C4⋊C412yes—
133C3⋊Dic3—24no—
134C3⋊Dic3C2×C4⋊C412yes—
135C3⋊Dic3C2×C4⋊C412yes—
136C23×C4—91no—
137C23×C4—92no—
138#117—91no—
139#117—92no—
140#117—92no—
141#117—92no—
142#117—184no—
143#117#15711yescharacteristic, complemented
144C2×C4⋊C4—92no—
145C2×C4⋊C4—92no—
146C2×C4⋊C4—98no—
147C2×C22⋊C4—92no—
148C2×C22⋊C4—92no—
149C2×C42—92no—
150C2×C42—92no—
151C2×C42—92no—
152C2×C42—92no—
153C2×C42—184no—
154#95—98no—
155C23×C3—22no—
156C22×D3—62no—
157C22×D3—62no—
158C22×D3—64no—
159C22×D3—64no—
160C22×D3—128no—
161C2×C3×C4—22no—
162C2×C3×C4—28no—
163C2×C3×C4—22no—
164C2×C3×C4—28no—
165C2×Dic3—68no—
166C2×Dic3—62no—
167C2×Dic3—62no—
168C2×Dic3—68no—
169C4×D3—68no—
170C4×D3—68no—
171C4×D3—64no—
172C4×D3—64no—
173C4×D3—64no—
174C4×D3—64no—
175C4×D3—1216no—
176C2×C32—22no—
177C2×C32C22×C4⋊C411yescharacteristic
178C2×C32C4×#4112yes—
179C3⋊D3—22no—
180C3⋊D3#52512yes—
181C3⋊D3#53312yes—
182C24—91no—
183C22×C4—91no—
184C22×C4—91no—
185C22×C4—91no—
186C22×C4—91no—
187C22×C4—91no—
188C22×C4—94no—
189C22×C4—94no—
190C22×C4—94no—
191C22×C4—94no—
192C22×C4—94no—
193C22×C4—188no—
194C22×C4—184no—
195C22×C4C2×#15711yescharacteristic
196C4⋊C4—94no—
197C4⋊C4—92no—
198C4⋊C4—184no—
199C4⋊C4—1816no—
200C4⋊C4C2×#15712yescomplemented
201C22⋊C4—92no—
202C22⋊C4—94no—
203C22⋊C4—184no—
204C22⋊C4C2×#15712yes—
205C42—94no—
206C42—92no—
207C42—184no—
208C42—184no—
209C42—184no—
210C42C2×#15712yescomplemented
211C22×C3—24no—
212C22×C3—22no—
213C22×C3—44no—
214C2×D3—62no—
215C2×D3—62no—
216C2×D3—68no—
217C2×D3—64no—
218C2×D3—128no—
219C2×D3—128no—
220C2×D3—124no—
221C3×C4—24no—
222C3×C4—24no—
223C3×C4—48no—
224Dic3—64no—
225Dic3—64no—
226Dic3—128no—
227C32#229611yescharacteristic, complemented, Sylow
228C23—91no—
229C23—92no—
230C23—92no—
231C23—91no—
232C23—184no—
233C23C22×#15711yescharacteristic
234C2×C4—94no—
235C2×C4—91no—
236C2×C4—91no—
237C2×C4—92no—
238C2×C4—92no—
239C2×C4—92no—
240C2×C4—94no—
241C2×C4—92no—
242C2×C4—94no—
243C2×C4—98no—
244C2×C4—94no—
245C2×C4—188no—
246C2×C4—184no—
247C2×C4—184no—
248C2×C4—1816no—
249C2×C4—184no—
250C2×C4—188no—
251C2×C4C4⋊#15714yescomplemented
252C2×C4C22×#15714yes—
253C2×C4C22×#15711yescharacteristic
254C2×C4C22×#15711yescharacteristic
255C2×C3—22no—
256C2×C3—24no—
257C2×C3—44no—
258D3—64no—
259D3—64no—
260D3—124no—
261C22—22no—
262C22—91no—
263C22—91no—
264C22—94no—
265C22—92no—
266C22—184no—
267C22—184no—
268C22—182no—
269C22C2×C4⋊#15712yes—
270C22C23×#15711yescharacteristic
271C4—24no—
272C4—92no—
273C4—92no—
274C4—188no—
275C4—184no—
276C4—364no—
277C4C2×C4⋊#15712yes—
278C4C2×C4⋊#15712yes—
279C3—22no—
280C2—22no—
281C2—92no—
282C2—92no—
283C2—182no—
284C2C22×C4⋊#15711yescharacteristic
285C2#41×#15712yes—
subgroupG/H
centerC2×C4C22×#157
commutator, socleC22×C32C23×C4
FrattiniC22C23×#157
FittingC32×#117C4
prime radicalC23×C3⋊D3C23
cosocleC22×C3⋊D3C24
hypercenter#117#157
hypocenterC32#2296
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
4. #10593759C2semidirect
6. C4×C4⋊#157C2semidirect
17. C32×#117C4semidirect
18. #64135C4semidirect
19. #64101C4semidirect
22. #64086C4semidirect
23. #64081C4semidirect
47. C32×C4⋊C4C2×C4semidirect
49. C32×C42C2×C4semidirect
52. C4⋊(C3⋊Dic3)C2×C4semidirect
53. #3750C2×C4semidirect
54. C4×C3⋊Dic3C2×C4semidirect
55. C4×C3⋊Dic3C2×C4semidirect
78. C2×C32×C4C4⋊C4semidirect
82. C2×C3⋊Dic3C4⋊C4semidirect
87. C4×C3⋊D3C4⋊C4semidirect
88. C4×C3⋊D3C4⋊C4semidirect
143. #117#157semidirect
200. C4⋊C4C2×#157semidirect
210. C42C2×#157semidirect
227. C32#2296semidirect
251. C2×C4C4⋊#157semidirect

Maximal subgroups

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

subgroupindex
C2×#642862
C22×C4×#1572
C3⋊D3×#1172
#105937592
#105937462
C4×C4⋊#1572
#22969