Finite Group Databasebeta

← D149⋊(Q8⋊C8) #34059980

Subgroups — D149⋊(Q8⋊C8) #34059980

Order 19072.

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

normal subgroups only

This group has 280 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
2C4×D149⋊C8C211yesmaximal, characteristic
3#23750475C212yesmaximal, complemented
4Q8⋊#11924753C212yesmaximal, complemented
5C4×Q8×D149C211yesmaximal, characteristic
6C2×D149⋊C8—21no—
7C2×D149⋊C8—21no—
8#18011978—21no—
9C4⋊#11924753C2212yes—
10C4×#11924753—21no—
11C4×#11924753C2212yes—
12C2×Q8×D149C411yescharacteristic
13Q8×Dic149C2211yescharacteristic
14C4×Dic298—21no—
15C4×Dic298C411yescharacteristic
16#18011876—21no—
17#18011876C2211yescharacteristic
18C4⋊C4×D149—21no—
19C4⋊C4×D149C411yescharacteristic
20C42×D149—21no—
21C42×D149C2211yescharacteristic
22C4×Q8×C149C411yescharacteristic
23D149⋊C8—24no—
24D149⋊C8—42no—
25C2×#11924753—22no—
26C2×#11924753—22no—
27C2×Dic298—21no—
28C2×Dic298C2×C411yescharacteristic
29Q8×D149—22no—
30Q8×D149C814yescomplemented
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#14558715—21no—
39#14558715—21no—
40#14558715—21no—
41C4×Dic149—21no—
42C4×Dic149—21no—
43C4×Dic149—21no—
44C4×Dic149D411yescharacteristic
45C4×Dic149D411yescharacteristic
46C4×Dic149C2311yescharacteristic
47C2×Q8×C149C2×C411yescharacteristic
48C4⋊C4×C149—21no—
49C4⋊C4×C149C2×C411yescharacteristic
50C42×C149—21no—
51C42×C149C2×C411yescharacteristic
52#11924753—24no—
53#11924753—42no—
54C22×D149C22⋊C411yescharacteristic
55Dic298—21no—
56Dic298—24no—
57Dic298C2×C812yescomplemented
58C2×Dic149—21no—
59C2×Dic149—21no—
60C2×Dic149C22⋊C411yescharacteristic
61C2×Dic149C2×D411yescharacteristic
62C2×Dic149C2×D411yescharacteristic
63C4×D149—24no—
64C4×D149—22no—
65C4×D149—42no—
66C4×D149C2×C812yes—
67C4×D149M1612yes—
68C4×D149SD1612yes—
69C4×D149Q1612yes—
70Q8×C149—21no—
71Q8×C149C2×C812yescomplemented
72C2×C4×C149—21no—
73C2×C4×C149—21no—
74C2×C4×C149C22⋊C411yescharacteristic
75C2×C4×C149C22⋊C411yescharacteristic
76C2×C4×C149C22×C411yescharacteristic
77C22×C149C2×C22⋊C411yescharacteristic
78C2×D149C22⋊C812yes—
79C2×D149#10312yes—
80C2×D149#10412yes—
81C4×C149—22no—
82C4×C149—21no—
83C4×C149—41no—
84C4×C149#10312yes—
85C4×C149C22×C811yescharacteristic
86C4×C149C2×M1611yescharacteristic
87Dic149—22no—
88Dic149—21no—
89Dic149—41no—
90Dic149C22⋊C812yes—
91Dic149C2×SD1611yescharacteristic
92Dic149C2×Q1611yescharacteristic
93C2×C149C2×C22⋊C811yescharacteristic
94C2×C149C2×#10311yescharacteristic
95C2×C149C2×#10411yescharacteristic
96D149Q8⋊C814yescomplemented
97C149C2×Q8⋊C811yescharacteristic, complemented, Sylow
98C2×Q8⋊C8—1491nomaximal, Sylow
99C2×C4×Q8—1491no—
100C2×C4⋊C8—1491no—
101C2×C4×C8—1491no—
102Q8⋊C8—1492no—
103Q8⋊C8—1492no—
104C22×Q8—1491no—
105C22×C8—2981no—
106C22×C8—2981no—
107C4×Q8—2981no—
108C4×Q8—2981no—
109C4×Q8—1491no—
110C4×Q8—1491no—
111C4×Q8—1491no—
112C4×Q8#1059701011yescharacteristic
113C2×C4⋊C4—2981no—
114C2×C4⋊C4—1491no—
115C2×C42—2981no—
116C2×C42—1491no—
117C4⋊C8—2981no—
118C4⋊C8—1492no—
119C4×C8—2981no—
120C4×C8—1492no—
121C2×Q8—2981no—
122C2×Q8—2982no—
123C2×Q8—1494no—
124C2×Q8—1491no—
125C2×Q8C2×#1059701011yescharacteristic
126C22×C4—2981no—
127C22×C4—2981no—
128C22×C4—1491no—
129C22×C4—1491no—
130C22×C4—1491no—
131C2×C8—2984no—
132C2×C8—2982no—
133C2×C8—2982no—
134C2×C8—5962no—
135C4⋊C4—21no—
136C4⋊C4—2981no—
137C4⋊C4—2981no—
138C4⋊C4—2981no—
139C4⋊C4—2981no—
140C4⋊C4—1491no—
141C4⋊C4C2×#1059701011yescharacteristic
142C42—21no—
143C42—2981no—
144C42—2981no—
145C42—2981no—
146C42—1491no—
147C42—1491no—
148C42—1491no—
149C42C2×#1059701011yescharacteristic
150C23—1491no—
151Q8—21no—
152Q8—2984no—
153Q8—2981no—
154Q8—1492no—
155Q8D149⋊C812yescomplemented
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—2982no—
159C2×C4—2984no—
160C2×C4—2981no—
161C2×C4—2981no—
162C2×C4—5962no—
163C2×C4—1491no—
164C2×C4—1491no—
165C2×C4—1491no—
166C2×C4—1492no—
167C2×C4—1492no—
168C2×C4—1492no—
169C2×C4—1492no—
170C2×C4C22⋊#1059701011yescharacteristic
171C2×C4C22⋊#1059701011yescharacteristic
172C2×C4C22×#1059701011yescharacteristic
173C8—2984no—
174C8—5962no—
175C22—1492no—
176C22—1492no—
177C22—1492no—
178C22C2×C22⋊#1059701011yescharacteristic
179C4—22no—
180C4—21no—
181C4—41no—
182C4—2982no—
183C4—2981no—
184C4—5961no—
185C4—1492no—
186C4—1491no—
187C4—1491no—
188C4#1801197412yes—
189C4C2×D149⋊C811yescharacteristic
190C4D149⋊M1611yescharacteristic
191C2—1494no—
192C2D149⋊(C22⋊C8)11yescharacteristic
193C2C2×#1801197411yescharacteristic
194C2D149⋊#10411yescharacteristic
subgroupG/H
centerC2×C4C22⋊#10597010
commutatorC4×C149C22×C8
FrattiniC2×C4C22×#10597010
FittingC4×Q8×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC22×D149C22⋊C4
cosocleC4×Dic149C23
hypercenterC4×Q8#10597010
hypocenterC149C2×Q8⋊C8
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
3. #23750475C2semidirect
4. Q8⋊#11924753C2semidirect
30. Q8×D149C8semidirect
57. Dic298C2×C8semidirect
71. Q8×C149C2×C8semidirect
96. D149Q8⋊C8semidirect
97. C149C2×Q8⋊C8semidirect
155. Q8D149⋊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
#237504752
Q8⋊#119247532
C4×Q8×D1492
C2×Q8⋊C8149