Finite Group Databasebeta

← #23750153

Subgroups — #23750153

Order 9536.

234 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 99 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
1#18011906C211yesmaximal, characteristic, complemented
2#18011904C211yesmaximal, characteristic, complemented
3#18011901C211yesmaximal, characteristic, complemented
4#18011897C211yesmaximal, characteristic, complemented
5#18011896C211yesmaximal, characteristic, complemented
6#18011893C211yesmaximal, characteristic, complemented
7#18011889C211yesmaximal, characteristic, complemented
8#18011884C211yesmaximal, characteristic
9C4×Dic298C211yesmaximal, characteristic, complemented
10C4×D596C211yesmaximal, characteristic, complemented
11C4×C22⋊D149C211yesmaximal, characteristic, complemented
12C4×C22⋊D149C211yesmaximal, characteristic, complemented
13#18011868C211yesmaximal, characteristic, complemented
14C42×D149C211yesmaximal, characteristic, complemented
15#117×C149C211yesmaximal, characteristic, complemented
16C2×Dic298C2211yescharacteristic
17C2×D596C2211yescharacteristic
18C2×C22⋊D149C2211yescharacteristic
19C2×C22⋊D149C2211yescharacteristic
20C2×C4×D149C2211yescharacteristic
21C2×C4×D149C2211yescharacteristic
22C2×C4×D149C2211yescharacteristic
23C2×C4×D149C2211yescharacteristic
24C4⋊Dic149C2211yescharacteristic
25C4⋊Dic149C2211yescharacteristic
26#14558715C2211yescharacteristic
27#14558715C2211yescharacteristic
28#14558715C2211yescharacteristic
29#14558715C2211yescharacteristic
30#14558715C2211yescharacteristic
31#14558715C2211yescharacteristic
32C22⋊Dic149C2211yescharacteristic
33C22⋊Dic149C2211yescharacteristic
34#14558713C2211yescharacteristic
35#14558713C2211yescharacteristic
36#14558713C2211yescharacteristic
37#14558713C2211yescharacteristic
38#14558713C2211yescharacteristic
39#14558713C2211yescharacteristic
40C4×Dic149C2211yescharacteristic
41C4×Dic149C2211yescharacteristic
42C4×Dic149C2211yescharacteristic
43C4×Dic149C2211yescharacteristic
44C22×C4×C149C2211yescharacteristic
45C4⋊C4×C149C2211yescharacteristic
46C4⋊C4×C149C2211yescharacteristic
47C22⋊C4×C149C2211yescharacteristic
48C22⋊C4×C149C2211yescharacteristic
49C42×C149C2211yescharacteristic
50C42×C149C2211yescharacteristic
51C22×D149C2311yescharacteristic
52C22×D149C2311yescharacteristic
53Dic298—22no—
54D596—22no—
55C22⋊D149—22no—
56C22⋊D149—22no—
57C2×Dic149C2311yescharacteristic
58C2×Dic149C2311yescharacteristic
59C2×Dic149C2311yescharacteristic
60C2×Dic149C2311yescharacteristic
61C2×Dic149C2311yescharacteristic
62C2×Dic149C2311yescharacteristic
63C4×D149—22no—
64C4×D149—22no—
65C4×D149—22no—
66C4×D149—22no—
67C23×C149C2311yescharacteristic
68C2×C4×C149—22no—
69C2×C4×C149C2311yescharacteristic
70C2×C4×C149C2311yescharacteristic
71C2×C4×C149C2311yescharacteristic
72C2×C4×C149C2311yescharacteristic
73C2×C4×C149C2311yescharacteristic
74C2×C4×C149C2311yescharacteristic
75C22×C149—21no—
76C22×C149—21no—
77C22×C149—21no—
78C22×C149C2411yescharacteristic
79C2×D149—21no—
80C2×D149—21no—
81C2×D149—21no—
82C2×D149—21no—
83C2×D149—21no—
84C2×D149#4112yes—
85C4×C149—21no—
86C4×C149—21no—
87C4×C149—21no—
88C4×C149—21no—
89C4×C149—21no—
90C4×C149#4112yes—
91Dic149—21no—
92Dic149—21no—
93Dic149—21no—
94Dic149—21no—
95Dic149—21no—
96Dic149#4112yes—
97C2×C149—41no—
98C2×C149C2×#4111yescharacteristic
99C2×C149C2×#4111yescharacteristic
100C2×C149C2×#4111yescharacteristic
101D149—22no—
102D149—41no—
103C149#52911yescharacteristic, complemented, Sylow
104#529—1491nomaximal, Sylow
105#126—1491no—
106#126—1491no—
107#125—1491no—
108#124—1491no—
109#123—1491no—
110#123—1491no—
111C22⋊Q8—1491no—
112#121—1491no—
113C4×Q8—1491no—
114C4×D4—1491no—
115C4×D4—1491no—
116C4×D4—1491no—
117#117—1491no—
118#117D14911yescharacteristic, complemented
119C2×C42—1491no—
120C2×Q8—1491no—
121C2×D4—1491no—
122C2×D4—1491no—
123C2×D4—1491no—
124C22×C4—1491no—
125C22×C4—1491no—
126C22×C4—1491no—
127C22×C4—1491no—
128C22×C4C2×D14911yescharacteristic
129C4⋊C4—1491no—
130C4⋊C4—1491no—
131C4⋊C4—1491no—
132C4⋊C4—1491no—
133C4⋊C4—1491no—
134C4⋊C4—1491no—
135C4⋊C4—1491no—
136C4⋊C4—1491no—
137C4⋊C4C2×D14911yescharacteristic
138C4⋊C4C2×D14911yescharacteristic
139C22⋊C4—1491no—
140C22⋊C4—1491no—
141C22⋊C4—1491no—
142C22⋊C4—1491no—
143C22⋊C4—1491no—
144C22⋊C4—1491no—
145C22⋊C4—1491no—
146C22⋊C4—1491no—
147C22⋊C4C2×D14911yescharacteristic
148C22⋊C4C2×D14911yescharacteristic
149C42—1491no—
150C42—1491no—
151C42—1491no—
152C42—1491no—
153C42C2×D14911yescharacteristic
154C42C2×D14911yescharacteristic
155C23—1491no—
156C23—1491no—
157C23C22×D14911yescharacteristic
158Q8—2982no—
159D4—2982no—
160D4—2982no—
161D4—2982no—
162C2×C4—22no—
163C2×C4—2982no—
164C2×C4—2982no—
165C2×C4—2982no—
166C2×C4—2982no—
167C2×C4—1491no—
168C2×C4—1491no—
169C2×C4—1491no—
170C2×C4—1491no—
171C2×C4—1491no—
172C2×C4—1491no—
173C2×C4C22×D14911yescharacteristic
174C2×C4C22×D14911yescharacteristic
175C2×C4C22×D14911yescharacteristic
176C2×C4C22×D14911yescharacteristic
177C2×C4C22×D14911yescharacteristic
178C2×C4C22×D14911yescharacteristic
179C22—21no—
180C22—21no—
181C22—21no—
182C22—2981no—
183C22—2981no—
184C22—2981no—
185C22—2981no—
186C22—2981no—
187C22—1492no—
188C22C23×D14911yescharacteristic
189C4—21no—
190C4—21no—
191C4—21no—
192C4—21no—
193C4—21no—
194C4—2981no—
195C4—2981no—
196C4—2981no—
197C4—2981no—
198C4—2981no—
199C4—1492no—
200C4#1455873612yes—
201C2—41no—
202C2—2982no—
203C2—5961no—
204C2#41×D14911yescharacteristic
205C2#41×D14911yescharacteristic
206C2C2×#1455873611yescharacteristic
subgroupG/H
centerC2×C4C22×D149
commutator, socle, cosocleC22×C149C24
FrattiniC22C23×D149
Fitting#117×C149C2
prime radical#18011884C2
hypercenter#117D149
hypocenterC149#529
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C2×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #18011906C2semidirect
2. #18011904C2semidirect
3. #18011901C2semidirect
4. #18011897C2semidirect
5. #18011896C2semidirect
6. #18011893C2semidirect
7. #18011889C2semidirect
9. C4×Dic298C2semidirect
10. C4×D596C2semidirect
11. C4×C22⋊D149C2semidirect
12. C4×C22⋊D149C2semidirect
13. #18011868C2semidirect
14. C42×D149C2semidirect
15. #117×C149C2semidirect
103. C149#529semidirect
118. #117D149semidirect