Finite Group Databasebeta

← #34059985

Subgroups — #34059985

Order 19072.

276 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 82 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#23750644C211yesmaximal, characteristic, complemented
2C4×D149⋊C8C211yesmaximal, characteristic, complemented
3Q8⋊#11924753C212yesmaximal, complemented
4#23750473C212yesmaximal, complemented
5C4×#14558737C211yesmaximal, characteristic
6C2×D149⋊C8—21no—
7C4⋊#11924753C2212yes—
8#18011968—21no—
9C4×#11924753—21no—
10C4×#11924753—21no—
11C4×#11924753C2212yes—
12C2×#14558737C411yescharacteristic
13Q8×Dic149C2211yescharacteristic
14C4×D596—21no—
15C4×D596C411yescharacteristic
16#18011873—21no—
17#18011873C2211yescharacteristic
18#18011869—21no—
19#18011869C411yescharacteristic
20C42×D149—21no—
21C42×D149C2211yescharacteristic
22C4×Q8×C149C411yescharacteristic
23D149⋊C8—24no—
24C2×#11924753—22no—
25C2×#11924753—22no—
26#14558737—22no—
27#14558737C814yescomplemented
28C2×D596—21no—
29C2×D596C2×C411yescharacteristic
30C2×C4×D149—21no—
31C2×C4×D149—21no—
32C2×C4×D149—21no—
33C2×C4×D149C2×C411yescharacteristic
34C2×C4×D149D411yescharacteristic
35C2×C4×D149D411yescharacteristic
36C4⋊Dic149—21no—
37C4⋊Dic149C2×C411yescharacteristic
38#14558713—21no—
39#14558713—21no—
40#14558713—21no—
41C4×Dic149—21no—
42C4×Dic149—21no—
43C4×Dic149D411yescharacteristic
44C4×Dic149D411yescharacteristic
45C4×Dic149C2311yescharacteristic
46C2×Q8×C149C2×C411yescharacteristic
47C4⋊C4×C149—21no—
48C4⋊C4×C149C2×C411yescharacteristic
49C42×C149—21no—
50C42×C149C2×C411yescharacteristic
51#11924753—24no—
52#11924753—42no—
53C22×D149—21no—
54C22×D149C22⋊C411yescharacteristic
55D596—24no—
56D596—21no—
57D596C2×C812yescomplemented
58C2×Dic149—21no—
59C2×Dic149C22⋊C411yescharacteristic
60C2×Dic149C2×D411yescharacteristic
61C2×Dic149C2×D411yescharacteristic
62C4×D149—22no—
63C4×D149—24no—
64C4×D149—22no—
65C4×D149—42no—
66C4×D149—42no—
67C4×D149C2×C812yes—
68C4×D149M1612yes—
69Q8×C149—21no—
70Q8×C149C2×C812yescomplemented
71C2×C4×C149—21no—
72C2×C4×C149—21no—
73C2×C4×C149C22⋊C411yescharacteristic
74C2×C4×C149C22⋊C411yescharacteristic
75C2×C4×C149C22×C411yescharacteristic
76C22×C149C2×C22⋊C411yescharacteristic
77C2×D149—21no—
78C2×D149—21no—
79C2×D149—22no—
80C2×D149—41no—
81C2×D149—41no—
82C2×D149C22⋊C812yes—
83C4×C149—22no—
84C4×C149—21no—
85C4×C149—41no—
86C4×C149#10412yes—
87C4×C149C22×C811yescharacteristic
88C4×C149C2×M1611yescharacteristic
89Dic149—21no—
90Dic149—41no—
91Dic149C22⋊C812yes—
92Dic149#13512yes—
93C2×C149C2×C22⋊C811yescharacteristic
94C2×C149#41611yescharacteristic
95C2×C149C2×#10411yescharacteristic
96D149—22no—
97D149—42no—
98C149#147611yescharacteristic, complemented, Sylow
99#1476—1491nomaximal, Sylow
100C4×#41—1491no—
101#431—1491no—
102C2×C4×C8—1491no—
103Q8⋊C8—1492no—
104D4⋊C8—1492no—
105C2×#41—1491no—
106C22×C8—2981no—
107C4×Q8—1491no—
108C4×Q8#1059701011yescharacteristic
109C4×D4—2981no—
110C4×D4—2981no—
111C4×D4—1491no—
112C4×D4—1491no—
113#117—2981no—
114#117—1491no—
115C2×C42—2981no—
116C2×C42—1491no—
117C4⋊C8—1492no—
118C22⋊C8—2981no—
119C4×C8—2981no—
120C4×C8—2981no—
121C4×C8—1492no—
122#41—2982no—
123#41—1494no—
124C2×Q8C2×#1059701011yescharacteristic
125C2×D4—2981no—
126C2×D4—1491no—
127C22×C4—2981no—
128C22×C4—2981no—
129C22×C4—2981no—
130C22×C4—1491no—
131C22×C4—1491no—
132C22×C4—1491no—
133C2×C8—2984no—
134C2×C8—2982no—
135C2×C8—2982no—
136C4⋊C4—21no—
137C4⋊C4—2981no—
138C4⋊C4—1491no—
139C4⋊C4C2×#1059701011yescharacteristic
140C22⋊C4—2981no—
141C22⋊C4—2981no—
142C22⋊C4—2981no—
143C42—21no—
144C42—2981no—
145C42—2981no—
146C42—1491no—
147C42—1491no—
148C42—1491no—
149C42C2×#1059701011yescharacteristic
150C23—2981no—
151C23—1491no—
152Q8—21no—
153Q8D149⋊C812yescomplemented
154D4—2984no—
155D4—2981no—
156D4—1492no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—2984no—
160C2×C4—2982no—
161C2×C4—2982no—
162C2×C4—2981no—
163C2×C4—5962no—
164C2×C4—5962no—
165C2×C4—1491no—
166C2×C4—1491no—
167C2×C4—1491no—
168C2×C4—1492no—
169C2×C4—1492no—
170C2×C4C22⋊#1059701011yescharacteristic
171C2×C4C22⋊#1059701011yescharacteristic
172C2×C4C22×#1059701011yescharacteristic
173C8—2984no—
174C8—5962no—
175C22—2981no—
176C22—2981no—
177C22—2982no—
178C22—5961no—
179C22—5961no—
180C22—1492no—
181C22C2×C22⋊#1059701011yescharacteristic
182C4—22no—
183C4—21no—
184C4—41no—
185C4—2981no—
186C4—5961no—
187C4—1492no—
188C4—1492no—
189C4#1801197612yes—
190C4C2×D149⋊C811yescharacteristic
191C4D149⋊M1611yescharacteristic
192C2—2982no—
193C2—5962no—
194C2D149⋊(C22⋊C8)11yescharacteristic
195C2#2375061511yescharacteristic
196C2C2×#1801197611yescharacteristic
subgroupG/H
centerC2×C4C22⋊#10597010
commutatorC4×C149C22×C8
FrattiniC2×C4C22×#10597010
FittingC4×Q8×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC2×#14558737C4
cosocleC4×Dic149C23
hypercenterC4×Q8#10597010
hypocenterC149#1476
LCSG ▷ C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #23750644C2semidirect
2. C4×D149⋊C8C2semidirect
3. Q8⋊#11924753C2semidirect
4. #23750473C2semidirect
27. #14558737C8semidirect
57. D596C2×C8semidirect
70. Q8×C149C2×C8semidirect
98. C149#1476semidirect
153. Q8D149⋊C8semidirect

Maximal subgroups

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

subgroupindex
#237506442
C4×D149⋊C82
Q8⋊#119247532
#237504732
C4×#145587372
#1476149