Finite Group Databasebeta

← #11858278

Subgroups — #11858278

Order 1152.

842 conjugacy classes of subgroups; only the 210 normal subgroups are shown.

normal subgroups only

This group has 842 conjugacy classes of subgroups — too many to draw. Only its 210 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×#64283C211yesmaximal, characteristic
2C22×#3787C211yesmaximal, characteristic
3C3⋊D3×#117C211yesmaximal, characteristic
4#10593755C214yesmaximal, complemented
5#10593743C214yesmaximal, complemented
6#10593726C214yesmaximal, complemented
7C22×C4×C3⋊D3C2211yescharacteristic
8C2×#3792C2212yes—
9C22×#622C2212yes—
10#64283—24no—
11C2×#3788C2212yes—
12C2×#3787—24no—
13C2×#3787C2212yes—
14C2×#3787C2212yes—
15C2×#3787C2212yes—
16C32×#117C411yescharacteristic
17#64135C411yescharacteristic
18#64101C2212yes—
19C4⋊C4×C3⋊D3C412yes—
20C22⋊C4×C3⋊D3C412yes—
21#64086C2212yes—
22#64081C412yes—
23C42×C3⋊D3C2212yes—
24#63779C2218yescomplemented
25C4⋊#622C2218yescomplemented
26D3×#117—62no—
27C23×C3⋊D3C2×C411yescharacteristic
28C22×C32×C4C2×C411yescharacteristic
29C22×C3⋊Dic3C2311yescharacteristic
30C2×C4×C3⋊D3C2×C414yes—
31C2×C4×C3⋊D3C2×C411yescharacteristic
32C2×C4×C3⋊D3C2×C411yescharacteristic
33C2×C4×C3⋊D3D414yes—
34C2×C4×C3⋊D3Q814yes—
35C2×C4×C3⋊D3C2311yescharacteristic
36C2×C4×C3⋊D3C2311yescharacteristic
37#3792—24no—
38C2×#622—24no—
39C2×#622C2314yes—
40C2×#622C2314yes—
41#3788—24no—
42#3787—24no—
43#3787—24no—
44#3787—24no—
45C32×C4⋊C4C2×C412yes—
46C32×C22⋊C4C2×C412yes—
47C32×C42C2×C412yes—
48#3757C2×C412yes—
49#3752C2×C414yes—
50C4⋊(C3⋊Dic3)C2×C412yes—
51#3750C2×C414yes—
52C4×C3⋊Dic3C2×C412yes—
53C4×C3⋊Dic3C2314yes—
54C2×#424—91nomaximal, Sylow
55C22×C4×D3—62no—
56C3×#117—22no—
57#926—62no—
58#892—64no—
59D3×C4⋊C4—64no—
60D3×C22⋊C4—64no—
61#877—64no—
62#872—64no—
63C42×D3—64no—
64C23×C32C22×C411yescharacteristic
65C22×C3⋊D3—24no—
66C22×C3⋊D3C4⋊C414yes—
67C22×C3⋊D3C22×C411yescharacteristic
68C22×C3⋊D3C22×C411yescharacteristic
69C2×C32×C4C4⋊C414yes—
70C2×C32×C4C22×C414yes—
71C2×C32×C4C22×C411yescharacteristic
72C2×C32×C4C22×C411yescharacteristic
73C2×C3⋊Dic3C22×C414yes—
74C2×C3⋊Dic3C22×C411yescharacteristic
75C2×C3⋊Dic3C2×D412yes—
76C2×C3⋊Dic3C2×Q812yes—
77C2×C3⋊Dic3C2411yescharacteristic
78C4×C3⋊D3—28no—
79C4×C3⋊D3C4⋊C414yes—
80C4×C3⋊D3C4⋊C414yes—
81C4×C3⋊D3C2×D412yes—
82C4×C3⋊D3C2×D412yes—
83C4×C3⋊D3C2×Q812yes—
84C4×C3⋊D3C2×Q812yes—
85#622—24no—
86#622—24no—
87C22×M16—91no—
88C23×C8—91no—
89C2×#117—91no—
90#424—94no—
91#424—94no—
92C2×C4⋊C8—94no—
93C23×D3—62no—
94C22×C3×C4—22no—
95C22×Dic3—62no—
96C2×C4×D3—62no—
97C2×C4×D3—62no—
98C2×C4×D3—62no—
99C2×C4×D3—62no—
100C2×C4×D3—68no—
101C2×C4×D3—68no—
102C2×C4×D3—68no—
103C3×C4⋊C4—24no—
104C3×C22⋊C4—24no—
105C3×C42—24no—
106#217—64no—
107(C2×D3)⋊C4—68no—
108C4⋊Dic3—64no—
109Dic3⋊C4—68no—
110C4×Dic3—64no—
111C4×Dic3—68no—
112C22×C32—22no—
113C22×C32C2×C4⋊C412yes—
114C22×C32C23×C411yescharacteristic
115C2×C3⋊D3—22no—
116C2×C3⋊D3—28no—
117C2×C3⋊D3C2×C4⋊C412yes—
118C2×C3⋊D3C2×C4⋊C412yes—
119C2×C3⋊D3#13114yes—
120C32×C4—24no—
121C32×C4C2×C4⋊C412yes—
122C32×C4C2×C4⋊C412yes—
123C3⋊Dic3—24no—
124C3⋊Dic3C2×C4⋊C412yes—
125C3⋊Dic3C22×D411yescharacteristic
126C3⋊Dic3C22×Q811yescharacteristic
127C23×C4—91no—
128C2×M16—92no—
129C2×M16—92no—
130C2×M16—184no—
131C22×C8—92no—
132C22×C8—92no—
133C22×C8—92no—
134C22×C8—92no—
135C22×C8—184no—
136#117—91no—
137#117—92no—
138#117—92no—
139#117—92no—
140#117#15711yescharacteristic
141C2×C4⋊C4—92no—
142C2×C22⋊C4—92no—
143C2×C42—92no—
144C4⋊C8—98no—
145C4⋊C8—98no—
146C23×C3—22no—
147C22×D3—62no—
148C22×D3—68no—
149C22×D3—62no—
150C22×D3—128no—
151C2×C3×C4—22no—
152C2×C3×C4—28no—
153C2×C3×C4—22no—
154C2×C3×C4—28no—
155C2×Dic3—62no—
156C2×Dic3—64no—
157C2×Dic3—64no—
158C2×Dic3—62no—
159C2×Dic3—68no—
160C4×D3—68no—
161C4×D3—68no—
162C4×D3—64no—
163C4×D3—64no—
164C4×D3—64no—
165C4×D3—64no—
166C4×D3—1216no—
167C2×C32—22no—
168C2×C32C22×C4⋊C411yescharacteristic
169C2×C32C2×#13112yes—
170C3⋊D3—22no—
171C3⋊D3#42414yescomplemented
172C24—91no—
173C22×C4—91no—
174C22×C4—91no—
175C22×C4—91no—
176C22×C4—91no—
177C22×C4—91no—
178C22×C4—94no—
179C22×C4—94no—
180C22×C4—94no—
181C22×C4C2×#15711yescharacteristic
182M16—184no—
183M16—184no—
184C2×C8—94no—
185C2×C8—94no—
186C2×C8—184no—
187C2×C8—184no—
188C2×C8—184no—
189C2×C8—184no—
190C4⋊C4—94no—
191C4⋊C4—92no—
192C4⋊C4C2×#15712yes—
193C22⋊C4—92no—
194C22⋊C4—94no—
195C22⋊C4C2×#15712yes—
196C42—94no—
197C42—92no—
198C42C2×#15712yes—
199C22×C3—24no—
200C22×C3—22no—
201C22×C3—44no—
202C2×D3—64no—
203C2×D3—68no—
204C2×D3—64no—
205C2×D3—1216no—
206C2×D3—124no—
207C3×C4—24no—
208C3×C4—24no—
209C3×C4—48no—
210Dic3—64no—
211Dic3—62no—
212Dic3—62no—
213Dic3—128no—
214C32C2×#42411yescharacteristic, complemented, Sylow
215C23—91no—
216C23—94no—
217C23—91no—
218C23—184no—
219C23C22×#15711yescharacteristic
220C2×C4—92no—
221C2×C4—92no—
222C2×C4—91no—
223C2×C4—91no—
224C2×C4—92no—
225C2×C4—92no—
226C2×C4—94no—
227C2×C4—92no—
228C2×C4—92no—
229C2×C4—94no—
230C2×C4—94no—
231C2×C4—188no—
232C2×C4C4⋊#15714yes—
233C2×C4C22×#15714yes—
234C2×C4C22×#15711yescharacteristic
235C2×C4C22×#15711yescharacteristic
236C8—184no—
237C8—184no—
238C2×C3—22no—
239C2×C3—24no—
240C2×C3—44no—
241D3—68no—
242D3—124no—
243C22—22no—
244C22—92no—
245C22—94no—
246C22—92no—
247C22—188no—
248C22—182no—
249C22C2×C4⋊#15712yes—
250C22C23×#15711yescharacteristic
251C4—24no—
252C4—91no—
253C4—92no—
254C4—91no—
255C4—184no—
256C4C2×C4⋊#15712yes—
257C4C2×C4⋊#15712yes—
258C3—22no—
259C2—22no—
260C2—94no—
261C2—182no—
262C2C22×C4⋊#15711yescharacteristic
263C2#1059664712yes—
subgroupG/H
centerC2×C4C22×#157
commutator, socleC22×C32C23×C4
FrattiniC22C23×#157
FittingC32×#117C4
prime radicalC23×C3⋊D3C2×C4
cosocleC2×C3⋊Dic3C24
hypercenter#117#157
hypocenterC32C2×#424
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
4. #10593755C2semidirect
5. #10593743C2semidirect
6. #10593726C2semidirect
24. #63779C22semidirect
25. C4⋊#622C22semidirect
171. C3⋊D3#424semidirect
214. C32C2×#424semidirect

Maximal subgroups

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

subgroupindex
C2×#642832
C22×#37872
C3⋊D3×#1172
#105937552
#105937432
#105937262
C2×#4249