Finite Group Databasebeta

← #34061547

Subgroups — #34061547

Order 19072.

464 conjugacy classes of subgroups; only the 168 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 168 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#23750660C212yesmaximal, complemented
2#23750656C214yesmaximal, complemented
3D4×#11924753C212yesmaximal, complemented
4#23750646C211yesmaximal, characteristic, complemented
5#23750642C211yesmaximal, characteristic, complemented
6#23750595C212yesmaximal, complemented
7C2×C22⋊#11924753C212yesmaximal, complemented
8C2×D4×Dic149C211yesmaximal, characteristic
9C2×#14558745C2214yescomplemented
10C22×#11924753C2214yescomplemented
11#18011978C2212yescomplemented
12C4⋊#11924753C2212yescomplemented
13C22⋊#11924753C2211yescharacteristic
14C22⋊#11924753C2212yes—
15C22⋊#11924753C2211yescharacteristic
16C22⋊#11924753C2214yescomplemented
17C22⋊#11924753C2214yescomplemented
18#18011966C2212yescomplemented
19C4×#11924753C2212yescomplemented
20C23×Dic149C2212yes—
21D4×Dic149C411yescharacteristic
22D4×Dic149C412yes—
23D4×Dic149C411yescharacteristic
24D4×Dic149C2212yes—
25D4×Dic149C2211yescharacteristic
26D4×Dic149C2211yescharacteristic
27C2×C4⋊Dic149C411yescharacteristic
28C2×C22⋊Dic149C412yes—
29C2×C4×Dic149C2211yescharacteristic
30C22×D4×C149C411yescharacteristic
31#14558745—44no—
32C2×#11924753—44no—
33C2×#11924753C2312yes—
34C2×#11924753C2312yes—
35C2×#11924753C2314yes—
36C22×Dic149—44no—
37C22×Dic149C2×C411yescharacteristic
38C22×Dic149C2×C412yes—
39C22×Dic149C2×C412yes—
40C22×Dic149C2×C412yes—
41C22×Dic149C2311yescharacteristic
42C22×Dic149C2312yes—
43C22×Dic149C2312yes—
44C4⋊Dic149C2×C412yes—
45C4⋊Dic149C2×C411yescharacteristic
46C4⋊Dic149C2×C411yescharacteristic
47C22⋊Dic149C2×C412yes—
48C22⋊Dic149C2×C412yes—
49C22⋊Dic149C2×C412yes—
50C22⋊Dic149C2×C412yes—
51C4×Dic149C2×C411yescharacteristic
52C4×Dic149C2×C411yescharacteristic
53C4×Dic149C2311yescharacteristic
54C4×Dic149C2311yescharacteristic
55C24×C149C2×C412yes—
56C2×D4×C149—24no—
57C2×D4×C149C2×C412yes—
58C2×D4×C149C2×C411yescharacteristic
59C2×D4×C149C2×C411yescharacteristic
60C22×C4×C149C2×C411yescharacteristic
61#11924753—22no—
62#11924753—24no—
63#11924753—22no—
64C2×Dic149—22no—
65C2×Dic149—22no—
66C2×Dic149—24no—
67C2×Dic149—24no—
68C2×Dic149—42no—
69C2×Dic149—42no—
70C2×Dic149—42no—
71C2×Dic149C22×C411yescharacteristic
72C2×Dic149C22×C412yes—
73C2×Dic149C22×C412yes—
74C2×Dic149C22×C411yescharacteristic
75C2×Dic149C22×C411yescharacteristic
76C2×Dic149C2411yescharacteristic
77C23×C149—24no—
78C23×C149—24no—
79C23×C149—42no—
80C23×C149C22×C412yes—
81C23×C149C22×C412yes—
82C23×C149C22×C411yescharacteristic
83D4×C149—24no—
84D4×C149—22no—
85D4×C149M1614yescomplemented
86C2×C4×C149—22no—
87C2×C4×C149C22×C411yescharacteristic
88C2×C4×C149C22×C411yescharacteristic
89C22×C149—21no—
90C22×C149—22no—
91C22×C149—21no—
92C22×C149—22no—
93C22×C149—22no—
94C22×C149—22no—
95C22×C149—22no—
96C22×C149—48no—
97C22×C149C2×M1614yes—
98C22×C149#13112yes—
99C22×C149C23×C411yescharacteristic
100C4×C149—21no—
101C4×C149C2×M1612yes—
102Dic149—21no—
103Dic149—22no—
104Dic149—22no—
105Dic149—21no—
106Dic149—21no—
107Dic149H(5,𝔽2)12yes—
108C2×C149—22no—
109C2×C149—24no—
110C2×C149—42no—
111C2×C149#51811yescharacteristic
112C2×C149C22×M1611yescharacteristic
113C2×C149C2×#13111yescharacteristic
114C149#297411yescharacteristic, complemented, Sylow
115#2974—1491nomaximal, Sylow
116C2×C4×D4—1491no—
117#436—1492no—
118#435—1494no—
119C8×D4—1492no—
120#432—1491no—
121#431—1491no—
122#407—1492no—
123C2×C22⋊C8—1492no—
124C22×D4#1059701011yescharacteristic
125C23×C4—1492no—
126C2×M16—1494no—
127C22×C8—1494no—
128C4×D4—1491no—
129C4×D4—1492no—
130C4×D4—1491no—
131C4×D4—1492no—
132C4×D4—1491no—
133C4×D4—1491no—
134C2×C4⋊C4—1491no—
135C2×C22⋊C4—1492no—
136C2×C42—1491no—
137C4⋊C8—1492no—
138C4⋊C8—1492no—
139C22⋊C8—1491no—
140C22⋊C8—1492no—
141C22⋊C8—1491no—
142C22⋊C8—1494no—
143C22⋊C8—1494no—
144#97—1492no—
145C4×C8—1492no—
146C24C2×#1059701012yes—
147C2×D4—24no—
148C2×D4C2×#1059701012yes—
149C2×D4C2×#1059701011yescharacteristic
150C2×D4C2×#1059701011yescharacteristic
151C22×C4—5964no—
152C22×C4—1491no—
153C22×C4—1491no—
154C22×C4—1492no—
155C22×C4—1492no—
156C22×C4—1492no—
157C22×C4—1492no—
158C22×C4—1492no—
159C22×C4C2×#1059701011yescharacteristic
160M16—5964no—
161C2×C8—5964no—
162C2×C8—1492no—
163C2×C8—1492no—
164C2×C8—1494no—
165C4⋊C4—1492no—
166C4⋊C4—1491no—
167C4⋊C4—1491no—
168C22⋊C4—1492no—
169C22⋊C4—1492no—
170C22⋊C4—1492no—
171C22⋊C4—1492no—
172C42—1491no—
173C42—1491no—
174C42—1491no—
175C42—1491no—
176C23—24no—
177C23—24no—
178C23—42no—
179C23C22×#1059701012yes—
180C23C22×#1059701012yes—
181C23C22×#1059701011yescharacteristic
182D4—24no—
183D4—22no—
184D4#1455874514yescomplemented
185C2×C4—22no—
186C2×C4—2982no—
187C2×C4—2984no—
188C2×C4—2984no—
189C2×C4—2982no—
190C2×C4—5962no—
191C2×C4—5962no—
192C2×C4—5962no—
193C2×C4—1491no—
194C2×C4—1491no—
195C2×C4—1491no—
196C2×C4—1492no—
197C2×C4—1492no—
198C2×C4—1491no—
199C2×C4C22×#1059701011yescharacteristic
200C2×C4C22×#1059701011yescharacteristic
201C8—2982no—
202C8—2984no—
203C8—2982no—
204C22—21no—
205C22—22no—
206C22—21no—
207C22—22no—
208C22—22no—
209C22—22no—
210C22—22no—
211C22—48no—
212C22C2×#1455874514yes—
213C22#1801199812yes—
214C22C23×#1059701011yescharacteristic
215C4—21no—
216C4—2981no—
217C4—2982no—
218C4—2982no—
219C4—2981no—
220C4—2981no—
221C4—1492no—
222C4C2×#1455874512yes—
223C2—22no—
224C2—24no—
225C2—42no—
226C2#2375069211yescharacteristic
227C2C22×#1455874511yescharacteristic
228C2C2×#1801199811yescharacteristic
subgroupG/H
center, FrattiniC22C23×#10597010
commutator, socleC22×C149C23×C4
Fitting, prime radicalC22×D4×C149C4
cosocleC2×Dic149C24
hypercenterC22×D4#10597010
hypocenterC149#2974
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #23750660C2semidirect
2. #23750656C2semidirect
3. D4×#11924753C2semidirect
4. #23750646C2semidirect
5. #23750642C2semidirect
6. #23750595C2semidirect
7. C2×C22⋊#11924753C2semidirect
9. C2×#14558745C22semidirect
10. C22×#11924753C22semidirect
11. #18011978C22semidirect
12. C4⋊#11924753C22semidirect
16. C22⋊#11924753C22semidirect
17. C22⋊#11924753C22semidirect
18. #18011966C22semidirect
19. C4×#11924753C22semidirect
85. D4×C149M16semidirect
114. C149#2974semidirect
184. D4#14558745semidirect

Maximal subgroups

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

subgroupindex
#237506602
#237506562
D4×#119247532
#237506462
#237506422
#237505952
C2×C22⋊#119247532
C2×D4×Dic1492
#2974149