Finite Group Databasebeta

← D149⋊(D4⋊C8) #34059977

Subgroups — D149⋊(D4⋊C8) #34059977

Order 19072.

344 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 94 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
1D149⋊(C4⋊C8)C211yesmaximal, characteristic, complemented
2C4×D149⋊C8C211yesmaximal, characteristic, complemented
3#23750473C212yesmaximal, complemented
4D4⋊#11924753C212yesmaximal, complemented
5C4×D4×D149C211yesmaximal, characteristic
6C2×D149⋊C8—21no—
7C2×D149⋊C8—21no—
8#18011978—21no—
9C4⋊#11924753C2212yescomplemented
10C4×#11924753—21no—
11C4×#11924753C2212yescomplemented
12C2×D4×D149C411yescharacteristic
13C22×C4×D149—21no—
14C4×D596C411yescharacteristic
15D4×Dic149C2211yescharacteristic
16#18011873C2211yescharacteristic
17C4×C22⋊D149—21no—
18#18011871—21no—
19C4⋊C4×D149C411yescharacteristic
20C22⋊C4×D149—21no—
21C42×D149C2211yescharacteristic
22C4×D4×C149C411yescharacteristic
23D149⋊C8—24no—
24D149⋊C8—42no—
25C2×#11924753—22no—
26C2×#11924753—22no—
27C23×D149—21no—
28C2×D596C2×C411yescharacteristic
29C2×C22⋊D149—21no—
30D4×D149—22no—
31D4×D149C814yescomplemented
32C22×Dic149—21no—
33C2×C4×D149—21no—
34C2×C4×D149—21no—
35C2×C4×D149—21no—
36C2×C4×D149—42no—
37C2×C4×D149—42no—
38C2×C4×D149C2×C411yescharacteristic
39C2×C4×D149D411yescharacteristic
40C2×C4×D149D411yescharacteristic
41C4⋊Dic149C2×C411yescharacteristic
42#14558715—21no—
43C22⋊Dic149—21no—
44#14558713—21no—
45#14558713—21no—
46C4×Dic149D411yescharacteristic
47C4×Dic149D411yescharacteristic
48C4×Dic149C2311yescharacteristic
49C2×D4×C149C2×C411yescharacteristic
50C22×C4×C149—21no—
51C4⋊C4×C149C2×C411yescharacteristic
52C22⋊C4×C149—21no—
53C42×C149C2×C411yescharacteristic
54#11924753—24no—
55#11924753—42no—
56C22×D149—21no—
57C22×D149—24no—
58C22×D149—42no—
59C22×D149—42no—
60C22×D149C22⋊C411yescharacteristic
61D596—21no—
62D596C2×C812yescomplemented
63C22⋊D149—24no—
64C2×Dic149—21no—
65C2×Dic149—41no—
66C2×Dic149—41no—
67C2×Dic149C22⋊C411yescharacteristic
68C2×Dic149C2×D411yescharacteristic
69C2×Dic149C2×D411yescharacteristic
70C4×D149—22no—
71C4×D149—42no—
72C4×D149—42no—
73C4×D149—41no—
74C4×D149—41no—
75C4×D149C2×C812yes—
76C4×D149M1612yes—
77C4×D149D812yes—
78C4×D149SD1612yes—
79C23×C149—21no—
80D4×C149—21no—
81D4×C149C2×C812yescomplemented
82C2×C4×C149—21no—
83C2×C4×C149—42no—
84C2×C4×C149C22⋊C411yescharacteristic
85C2×C4×C149C22⋊C411yescharacteristic
86C2×C4×C149C22×C411yescharacteristic
87C22×C149—22no—
88C22×C149—41no—
89C22×C149—41no—
90C22×C149C2×C22⋊C411yescharacteristic
91C2×D149—22no—
92C2×D149—41no—
93C2×D149—41no—
94C2×D149—48no—
95C2×D149C22⋊C812yes—
96C2×D149#10212yes—
97C2×D149#10412yes—
98C4×C149—21no—
99C4×C149—41no—
100C4×C149#10212yes—
101C4×C149C22×C811yescharacteristic
102C4×C149C2×M1611yescharacteristic
103Dic149—21no—
104Dic149—41no—
105Dic149C22⋊C812yes—
106Dic149C2×D811yescharacteristic
107Dic149C2×SD1611yescharacteristic
108C2×C149—42no—
109C2×C149C2×C22⋊C811yescharacteristic
110C2×C149C2×#10211yescharacteristic
111C2×C149C2×#10411yescharacteristic
112D149—42no—
113D149D4⋊C814yescomplemented
114C149C2×D4⋊C811yescharacteristic, complemented, Sylow
115C2×D4⋊C8—1491nomaximal, Sylow
116C2×C4×D4—1491no—
117C2×C4⋊C8—1491no—
118C2×C4×C8—1491no—
119D4⋊C8—1492no—
120D4⋊C8—1492no—
121C22×D4—1491no—
122C23×C4—2981no—
123C22×C8—2981no—
124C22×C8—2981no—
125C4×D4—2981no—
126C4×D4—2981no—
127C4×D4—1491no—
128C4×D4—1491no—
129C4×D4—1491no—
130C4×D4#1059701011yescharacteristic
131C2×C4⋊C4—1491no—
132C2×C22⋊C4—2981no—
133C2×C42—1491no—
134C4⋊C8—2981no—
135C4⋊C8—1492no—
136C4×C8—2981no—
137C4×C8—1492no—
138C24—2981no—
139C2×D4—2982no—
140C2×D4—2981no—
141C2×D4—1494no—
142C2×D4—1491no—
143C2×D4C2×#1059701011yescharacteristic
144C22×C4—21no—
145C22×C4—2981no—
146C22×C4—2981no—
147C22×C4—2981no—
148C22×C4—2981no—
149C22×C4—5962no—
150C22×C4—5962no—
151C22×C4—1491no—
152C22×C4—1491no—
153C22×C4—1491no—
154C2×C8—2984no—
155C2×C8—2982no—
156C2×C8—2982no—
157C2×C8—5962no—
158C4⋊C4—2981no—
159C4⋊C4—1491no—
160C4⋊C4C2×#1059701011yescharacteristic
161C22⋊C4—21no—
162C22⋊C4—2981no—
163C22⋊C4—2981no—
164C22⋊C4—2981no—
165C42—1491no—
166C42—1491no—
167C42—1491no—
168C42C2×#1059701011yescharacteristic
169C23—21no—
170C23—2984no—
171C23—2981no—
172C23—5962no—
173C23—5962no—
174C23—1491no—
175D4—21no—
176D4—2984no—
177D4—2981no—
178D4—1492no—
179D4D149⋊C812yescomplemented
180C2×C4—21no—
181C2×C4—42no—
182C2×C4—2982no—
183C2×C4—2981no—
184C2×C4—5962no—
185C2×C4—5961no—
186C2×C4—5961no—
187C2×C4—5961no—
188C2×C4—5961no—
189C2×C4—5962no—
190C2×C4—1491no—
191C2×C4—1491no—
192C2×C4—1491no—
193C2×C4—1492no—
194C2×C4—1492no—
195C2×C4—1492no—
196C2×C4—1492no—
197C2×C4C22⋊#1059701011yescharacteristic
198C2×C4C22⋊#1059701011yescharacteristic
199C2×C4C22×#1059701011yescharacteristic
200C8—2984no—
201C8—5962no—
202C22—22no—
203C22—41no—
204C22—41no—
205C22—2982no—
206C22—5968no—
207C22—5961no—
208C22—5961no—
209C22—1492no—
210C22—1492no—
211C22—1492no—
212C22C2×C22⋊#1059701011yescharacteristic
213C4—21no—
214C4—41no—
215C4—2981no—
216C4—5961no—
217C4—1492no—
218C4—1491no—
219C4—1491no—
220C4#1801197312yes—
221C4C2×D149⋊C811yescharacteristic
222C4D149⋊M1611yescharacteristic
223C2—42no—
224C2—5962no—
225C2—1494no—
226C2D149⋊(C22⋊C8)11yescharacteristic
227C2C2×#1801197311yescharacteristic
228C2D149⋊#10411yescharacteristic
subgroupG/H
centerC2×C4C22⋊#10597010
commutatorC4×C149C22×C8
FrattiniC2×C4C22×#10597010
FittingC4×D4×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC2×D4×D149C4
cosocleC4×Dic149C23
hypercenterC4×D4#10597010
hypocenterC149C2×D4⋊C8
LCSG ▷ C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. D149⋊(C4⋊C8)C2semidirect
2. C4×D149⋊C8C2semidirect
3. #23750473C2semidirect
4. D4⋊#11924753C2semidirect
9. C4⋊#11924753C22semidirect
11. C4×#11924753C22semidirect
31. D4×D149C8semidirect
62. D596C2×C8semidirect
81. D4×C149C2×C8semidirect
113. D149D4⋊C8semidirect
114. C149C2×D4⋊C8semidirect
179. D4D149⋊C8semidirect

Maximal subgroups

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

subgroupindex
D149⋊(C4⋊C8)2
C4×D149⋊C82
#237504732
D4⋊#119247532
C4×D4×D1492
C2×D4⋊C8149