Finite Group Databasebeta

← #34060852

Subgroups — #34060852

Order 19072.

316 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 68 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⋊#108C211yesmaximal, characteristic, complemented
2#23750617C212yesmaximal, complemented
3D149⋊#100C212yesmaximal, complemented
4#23750588C211yesmaximal, characteristic, complemented
5C2×D8×D149C211yesmaximal, characteristic
6D149⋊M16C2212yes—
7D149⋊M16C2211yescharacteristic
8#18011990C2211yescharacteristic
9#18011982—21no—
10#18011981—21no—
11#18011973—24no—
12#18011971—24no—
13#18011965—21no—
14C8×#10597010—21no—
15C2×D4×D149C2212yes—
16C2×D1192C411yescharacteristic, complemented
17C2×#14558721C412yescomplemented
18D8×D149—21no—
19D8×D149—21no—
20D8×D149—21no—
21D8×D149—21no—
22C2×C8×D149C2211yescharacteristic
23C2×D8×C149C411yescharacteristic, complemented
24#14558746—22no—
25#14558746—21no—
26#14558745—22no—
27#14558745D412yes—
28D149⋊C8—21no—
29D149⋊C8—22no—
30C4⋊#10597010D412yes—
31C22⋊#10597010—21no—
32C4×#10597010—21no—
33C23×D149—22no—
34C2×D596C2×C412yes—
35C2×C22⋊D149—22no—
36D4×D149—22no—
37D4×D149—22no—
38D4×D149—22no—
39D4×D149—22no—
40C2×C4×D149C2311yescharacteristic
41D1192—21no—
42D1192—21no—
43#14558721—22no—
44#14558721—22no—
45C2×#11924746C2×C411yescharacteristic
46C8×D149D411yescharacteristic
47C8×D149D411yescharacteristic
48C8×D149D411yescharacteristic
49C8×D149D411yescharacteristic
50C2×D4×C149C2×C412yes—
51D8×C149—21no—
52D8×C149—21no—
53C2×C8×C149C2×C411yescharacteristic
54C2×#10597010—22no—
55#11924753—22no—
56#11924753—42no—
57C22×D149—22no—
58C22×D149—42no—
59C22×D149—42no—
60C22×D149—84no—
61C22×D149#4111yescharacteristic
62D596—22no—
63D596—22no—
64C22⋊D149—42no—
65C22⋊D149—42no—
66C2×Dic149C2×D411yescharacteristic
67C4×D149C2×D411yescharacteristic
68C4×D149C2×D411yescharacteristic
69C4×D149C2×D411yescharacteristic
70C4×D149#4111yescharacteristic
71#11924746C22⋊C411yescharacteristic
72#11924746C22⋊C411yescharacteristic
73C23×C149—22no—
74D4×C149—22no—
75D4×C149—22no—
76C2×C4×C149C22×C411yescharacteristic
77C8×C149C22⋊C411yescharacteristic
78C8×C149C22⋊C411yescharacteristic
79C22×C149—42no—
80C22×C149—82no—
81C22×C149C4×D411yescharacteristic
82C2×D149—22no—
83C2×D149—42no—
84C2×D149—84no—
85C2×D149—84no—
86C2×D149—82no—
87C2×D149#12111yescharacteristic
88C2×D149#12411yescharacteristic
89#10597010—42no—
90C4×C149C2×C22⋊C411yescharacteristic
91C4×C149C4×D411yescharacteristic
92Dic149#12111yescharacteristic
93Dic149#12711yescharacteristic
94C2×C149—21no—
95C2×C149—82no—
96C2×C149#39011yescharacteristic
97D149—21no—
98D149—82no—
99D149#47212yes—
100C149#197811yescharacteristic, complemented, Sylow
101#1978—1491nomaximal, Sylow
102C22×D8—1491no—
103C2×#108—1491no—
104#418—1492no—
105C2×#100—1492no—
106#405—1491no—
107C22×D4—1492no—
108C2×D8—2981no—
109C2×D8—2981no—
110C2×D8—2981no—
111C2×D8—2981no—
112C2×D8—1492no—
113C2×D8—1491no—
114C2×D8#1059701011yescharacteristic, complemented
115C2×M16—1492no—
116C2×M16—1491no—
117C22×C8—1491no—
118#117—1491no—
119#108—2981no—
120#108—2981no—
121#102—2984no—
122#100—2984no—
123#97—2981no—
124C4×C8—2981no—
125C24—2982no—
126C2×D4—2982no—
127C2×D4—2982no—
128C2×D4—2982no—
129C2×D4—2982no—
130C2×D4—2982no—
131C2×D4—1492no—
132C2×D4C2×#1059701012yes—
133C22×C4—1491no—
134D8—21no—
135D8—21no—
136D8—2982no—
137D8—2982no—
138D8—2981no—
139D8—2981no—
140M16—2981no—
141M16—2982no—
142M16—2982no—
143M16—1492no—
144C2×C8—2981no—
145C2×C8—2982no—
146C2×C8—1491no—
147C2×C8—1491no—
148C2×C8—1491no—
149C2×C8—1491no—
150C2×C8—1491no—
151C2×C8C2×#1059701011yescharacteristic
152C4⋊C4—1492no—
153C22⋊C4—2981no—
154C42—2981no—
155C23—22no—
156C23—2982no—
157C23—5962no—
158C23—5962no—
159C23—1491no—
160C23—11924no—
161D4—22no—
162D4—22no—
163D4—2982no—
164D4—2982no—
165D4—5962no—
166D4—5962no—
167C2×C4—2982no—
168C2×C4—1491no—
169C2×C4—1491no—
170C2×C4—1491no—
171C2×C4—1491no—
172C2×C4—1491no—
173C2×C4C22×#1059701011yescharacteristic
174C8—2982no—
175C8—5962no—
176C8—1491no—
177C8—1491no—
178C8C22⋊#1059701011yescharacteristic
179C8C22⋊#1059701011yescharacteristic
180C22—42no—
181C22—82no—
182C22—2982no—
183C22—5962no—
184C22—1491no—
185C22—1491no—
186C22—11922no—
187C22—11924no—
188C22—11924no—
189C22D4×#1059701011yescharacteristic
190C4—5962no—
191C4—1491no—
192C4—1491no—
193C4C2×C22⋊#1059701011yescharacteristic
194C4D4×#1059701011yescharacteristic
195C2—21no—
196C2—82no—
197C2—2981no—
198C2—1492no—
199C2—11922no—
200C2#2375057711yescharacteristic
subgroupG/H
centerC2#23750577
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC2×D8×C149C4
socleC2×C149#390
prime radicalC2×D8×D149C2
cosocleC2×C4×D149C23
hypercenterC2×D8#10597010
hypocenterC149#1978
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. D149⋊#108C2semidirect
2. #23750617C2semidirect
3. D149⋊#100C2semidirect
4. #23750588C2semidirect
16. C2×D1192C4semidirect
17. C2×#14558721C4semidirect
23. C2×D8×C149C4semidirect
100. C149#1978semidirect
114. C2×D8#10597010semidirect

Maximal subgroups

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

subgroupindex
D149⋊#1082
#237506172
D149⋊#1002
#237505882
C2×D8×D1492
#1978149