Finite Group Databasebeta

← #34060023

Subgroups — #34060023

Order 19072.

246 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 66 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#23750647C211yesmaximal, characteristic, complemented
2#23750644C211yesmaximal, characteristic, complemented
3#23750475C212yesmaximal, complemented
4D4⋊#11924753C212yesmaximal, complemented
5C4×#14558735C211yesmaximal, characteristic
6C4⋊#11924753—21no—
7C4⋊#11924753C2212yes—
8#18011968—21no—
9#18011968—21no—
10#18011966—21no—
11C4×#11924753C2212yes—
12C2×#14558735C411yescharacteristic
13C4×Dic298C411yescharacteristic
14#18011876C2211yescharacteristic
15D4×Dic149C2211yescharacteristic
16C4×C22⋊D149—21no—
17#18011871—21no—
18#18011869C411yescharacteristic
19#18011867—21no—
20C2×C4×Dic149—21no—
21C42×D149C2211yescharacteristic
22C4×D4×C149C411yescharacteristic
23C2×#11924753—22no—
24C2×#11924753—22no—
25#14558735—22no—
26#14558735—22no—
27C2×Dic298C2×C411yescharacteristic
28C2×C22⋊D149—21no—
29C22×Dic149—21no—
30C22×Dic149—21no—
31C2×C4×D149C2×C411yescharacteristic
32C2×C4×D149D411yescharacteristic
33C2×C4×D149D411yescharacteristic
34C4⋊Dic149C2×C411yescharacteristic
35#14558715—21no—
36#14558715—21no—
37C22⋊Dic149—21no—
38#14558713—21no—
39C4×Dic149—21no—
40C4×Dic149—21no—
41C4×Dic149—21no—
42C4×Dic149D411yescharacteristic
43C4×Dic149D411yescharacteristic
44C4×Dic149C2311yescharacteristic
45C2×D4×C149C2×C411yescharacteristic
46C22×C4×C149—21no—
47C4⋊C4×C149C2×C411yescharacteristic
48C22⋊C4×C149—21no—
49C42×C149C2×C411yescharacteristic
50#11924753—42no—
51#11924753—42no—
52C22×D149C22⋊C411yescharacteristic
53Dic298—21no—
54Dic298M1612yes—
55C22⋊D149—24no—
56C2×Dic149—24no—
57C2×Dic149—21no—
58C2×Dic149—21no—
59C2×Dic149—42no—
60C2×Dic149C22⋊C411yescharacteristic
61C2×Dic149C2×D411yescharacteristic
62C2×Dic149C2×D411yescharacteristic
63C4×D149—21no—
64C4×D149—21no—
65C4×D149—22no—
66C4×D149—41no—
67C23×C149—21no—
68D4×C149—21no—
69D4×C149M1612yes—
70C2×C4×C149—21no—
71C2×C4×C149—42no—
72C2×C4×C149C22⋊C411yescharacteristic
73C2×C4×C149C22⋊C411yescharacteristic
74C2×C4×C149C22×C411yescharacteristic
75C22×C149—22no—
76C22×C149—41no—
77C22×C149—41no—
78C22×C149C2×C22⋊C411yescharacteristic
79C2×D149—21no—
80C2×D149—21no—
81C2×D149—21no—
82C4×C149—21no—
83C4×C149—21no—
84C4×C149—41no—
85C4×C149C2×M1611yescharacteristic
86C4×C149C2×M1611yescharacteristic
87Dic149—21no—
88Dic149—22no—
89Dic149—21no—
90Dic149—41no—
91Dic149#13512yes—
92C2×C149—42no—
93C2×C149#40711yescharacteristic
94C2×C149#41611yescharacteristic
95C2×C149#42111yescharacteristic
96D149—41no—
97C149#148811yescharacteristic, complemented, Sylow
98#1488—1491nomaximal, Sylow
99C4×#41—1491no—
100#432—1491no—
101#431—1491no—
102Q8⋊C8—1492no—
103D4⋊C8—1492no—
104C2×#41—1491no—
105C4×Q8—1491no—
106C4×Q8—1491no—
107C4×D4—2981no—
108C4×D4—2981no—
109C4×D4—1491no—
110C4×D4#1059701011yescharacteristic
111#117—2981no—
112#117—1491no—
113C2×C42—2981no—
114C2×C42—1491no—
115C4⋊C8—2981no—
116C4⋊C8—1492no—
117C22⋊C8—2981no—
118C22⋊C8—2981no—
119#97—2981no—
120C4×C8—1492no—
121#41—2982no—
122#41—2982no—
123C2×Q8—1491no—
124C2×D4—2981no—
125C2×D4C2×#1059701011yescharacteristic
126C22×C4—21no—
127C22×C4—2981no—
128C22×C4—2981no—
129C22×C4—1491no—
130C22×C4—1491no—
131C22×C4—1491no—
132C2×C8—2982no—
133C2×C8—2982no—
134C4⋊C4—2981no—
135C4⋊C4—2981no—
136C4⋊C4—1491no—
137C4⋊C4C2×#1059701011yescharacteristic
138C22⋊C4—21no—
139C22⋊C4—2981no—
140C22⋊C4—2981no—
141C42—2981no—
142C42—2981no—
143C42—2981no—
144C42—1491no—
145C42—1491no—
146C42—1491no—
147C42C2×#1059701011yescharacteristic
148C23—21no—
149C23—1491no—
150Q8—2981no—
151Q8—1492no—
152D4—21no—
153D4—2984no—
154D4#1455874612yes—
155C2×C4—21no—
156C2×C4—42no—
157C2×C4—2982no—
158C2×C4—2984no—
159C2×C4—2981no—
160C2×C4—2981no—
161C2×C4—2981no—
162C2×C4—2981no—
163C2×C4—5961no—
164C2×C4—5962no—
165C2×C4—1491no—
166C2×C4—1491no—
167C2×C4—1491no—
168C2×C4C22⋊#1059701011yescharacteristic
169C2×C4C22⋊#1059701011yescharacteristic
170C2×C4C22×#1059701011yescharacteristic
171C8—5962no—
172C8—5962no—
173C22—22no—
174C22—41no—
175C22—41no—
176C22—2981no—
177C22—2981no—
178C22—2981no—
179C22C2×C22⋊#1059701011yescharacteristic
180C4—21no—
181C4—21no—
182C4—41no—
183C4—2981no—
184C4—2982no—
185C4—2981no—
186C4—5961no—
187C4—1492no—
188C4D149⋊M1611yescharacteristic
189C4C2×#1455874611yescharacteristic
190C2—42no—
191C2—5961no—
192C2#2375059611yescharacteristic
193C2#2375061511yescharacteristic
194C2#2375062311yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC4×D4×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC2×#14558735C4
cosocleC4×Dic149C23
hypercenterC4×D4#10597010
hypocenterC149#1488
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #23750647C2semidirect
2. #23750644C2semidirect
3. #23750475C2semidirect
4. D4⋊#11924753C2semidirect
97. C149#1488semidirect

Maximal subgroups

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

subgroupindex
#237506472
#237506442
#237504752
D4⋊#119247532
C4×#145587352
#1488149