Finite Group Databasebeta

← #34060853

Subgroups — #34060853

Order 19072.

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

normal subgroups only

This group has 276 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
2#23750618C212yesmaximal
3D149⋊#101C212yesmaximal
4#23750588C211yesmaximal, characteristic
5C2×Q16×D149C211yesmaximal, characteristic
6D149⋊M16C2212yes—
7D149⋊M16C2211yescharacteristic
8#18011990C2211yescharacteristic
9#18011982—21no—
10#18011981—21no—
11#18011974—24no—
12#18011972—24no—
13#18011965—21no—
14C8×#10597010—21no—
15C2×Q8×D149C2212yes—
16C2×Dic596C411yescharacteristic, complemented
17C2×#14558726C412yescomplemented
18Q16×D149—21no—
19Q16×D149—21no—
20Q16×D149—21no—
21Q16×D149—21no—
22C2×C8×D149C2211yescharacteristic
23C2×Q16×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—
33C2×Dic298—22no—
34C2×Dic298C2×C412yes—
35Q8×D149—22no—
36Q8×D149—22no—
37Q8×D149—22no—
38Q8×D149—22no—
39C2×C4×D149—22no—
40C2×C4×D149C2311yescharacteristic
41Dic596—21no—
42Dic596—21no—
43#14558726—22no—
44#14558726—22no—
45C2×#11924746C2×C411yescharacteristic
46C8×D149D411yescharacteristic
47C8×D149D411yescharacteristic
48C8×D149D411yescharacteristic
49C8×D149D411yescharacteristic
50C2×Q8×C149C2×C412yes—
51Q16×C149—21no—
52Q16×C149—21no—
53C2×C8×C149C2×C411yescharacteristic
54C2×#10597010—22no—
55#11924753—22no—
56#11924753—42no—
57C22×D149#4111yescharacteristic
58Dic298—22no—
59Dic298—22no—
60Dic298—42no—
61Dic298—42no—
62C2×Dic149—22no—
63C2×Dic149C2×D411yescharacteristic
64C4×D149—42no—
65C4×D149—42no—
66C4×D149C2×D411yescharacteristic
67C4×D149C2×D411yescharacteristic
68C4×D149C2×D411yescharacteristic
69C4×D149#4111yescharacteristic
70#11924746C22⋊C411yescharacteristic
71#11924746C22⋊C411yescharacteristic
72Q8×C149—22no—
73Q8×C149—22no—
74C2×C4×C149—22no—
75C2×C4×C149C22×C411yescharacteristic
76C8×C149C22⋊C411yescharacteristic
77C8×C149C22⋊C411yescharacteristic
78C22×C149C4×D411yescharacteristic
79C2×D149—22no—
80C2×D149#12111yescharacteristic
81C2×D149#12411yescharacteristic
82#10597010—42no—
83C4×C149—42no—
84C4×C149C2×C22⋊C411yescharacteristic
85C4×C149C4×D411yescharacteristic
86Dic149—42no—
87Dic149#12111yescharacteristic
88Dic149#12711yescharacteristic
89C2×C149—21no—
90C2×C149#39011yescharacteristic
91D149—21no—
92D149#47312yes—
93C149#197911yescharacteristic, complemented, Sylow
94#1979—1491nomaximal, Sylow
95C22×Q16—1491no—
96C2×#108—1491no—
97#419—1492no—
98C2×#101—1492no—
99#405—1491no—
100C22×Q8—1492no—
101C2×Q16—2981no—
102C2×Q16—2981no—
103C2×Q16—2981no—
104C2×Q16—2981no—
105C2×Q16—1492no—
106C2×Q16—1491no—
107C2×Q16#1059701011yescharacteristic, complemented
108C2×M16—1492no—
109C2×M16—1491no—
110C22×C8—1491no—
111#117—1491no—
112#108—2981no—
113#108—2981no—
114#103—2984no—
115#101—2984no—
116#97—2981no—
117C4×C8—2981no—
118C2×Q8—2982no—
119C2×Q8—2982no—
120C2×Q8—2982no—
121C2×Q8—2982no—
122C2×Q8—2982no—
123C2×Q8—1492no—
124C2×Q8C2×#1059701012yes—
125C22×C4—2982no—
126C22×C4—1491no—
127Q16—21no—
128Q16—21no—
129Q16—2982no—
130Q16—2982no—
131Q16—2981no—
132Q16—2981no—
133M16—2981no—
134M16—2982no—
135M16—2982no—
136M16—1492no—
137C2×C8—2981no—
138C2×C8—2982no—
139C2×C8—1491no—
140C2×C8—1491no—
141C2×C8—1491no—
142C2×C8—1491no—
143C2×C8—1491no—
144C2×C8C2×#1059701011yescharacteristic
145C4⋊C4—1492no—
146C22⋊C4—2981no—
147C42—2981no—
148C23—1491no—
149Q8—22no—
150Q8—22no—
151Q8—2982no—
152Q8—2982no—
153Q8—5962no—
154Q8—5962no—
155C2×C4—22no—
156C2×C4—2982no—
157C2×C4—2982no—
158C2×C4—5962no—
159C2×C4—5962no—
160C2×C4—1491no—
161C2×C4—1491no—
162C2×C4—1491no—
163C2×C4—1491no—
164C2×C4—1491no—
165C2×C4C22×#1059701011yescharacteristic
166C8—2982no—
167C8—5962no—
168C8—1491no—
169C8—1491no—
170C8C22⋊#1059701011yescharacteristic
171C8C22⋊#1059701011yescharacteristic
172C22—2982no—
173C22—1491no—
174C22—1491no—
175C22D4×#1059701011yescharacteristic
176C4—42no—
177C4—5962no—
178C4—5962no—
179C4—1491no—
180C4—1491no—
181C4C2×C22⋊#1059701011yescharacteristic
182C4D4×#1059701011yescharacteristic
183C2—21no—
184C2—2981no—
185C2—1492no—
186C2#2375057711yescharacteristic
subgroupG/H
centerC2#23750577
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC2×Q16×C149C4
socleC2×C149#390
prime radicalC22×D149#41
cosocleC2×C4×D149C23
hypercenterC2×Q16#10597010
hypocenterC149#1979
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
16. C2×Dic596C4semidirect
17. C2×#14558726C4semidirect
23. C2×Q16×C149C4semidirect
93. C149#1979semidirect
107. C2×Q16#10597010semidirect

Maximal subgroups

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

subgroupindex
D149⋊#1082
#237506182
D149⋊#1012
#237505882
C2×Q16×D1492
#1979149