Finite Group Databasebeta

← #34046231

Subgroups — #34046231

Order 19072.

254 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 87 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
1C2×#18011842C211yesmaximal, characteristic
2C2×#18011836C211yesmaximal, characteristic
3C2×#18011834C211yesmaximal, characteristic
4#23749530C211yesmaximal, characteristic
5#23749494C211yesmaximal, characteristic
6#23749379C211yesmaximal, characteristic
7C2×#106×C149C211yesmaximal, characteristic
8C22×Dic298C2211yescharacteristic
9C22×#11924746C2211yescharacteristic
10C2×C4⋊Dic149C2211yescharacteristic
11C2×#14558715—22no—
12C2×C4×Dic149C2211yescharacteristic
13#18011842—22no—
14#18011836—22no—
15#18011834—22no—
16#18011818—22no—
17C22×C8×C149C2211yescharacteristic
18C2×C4⋊C4×C149C2211yescharacteristic
19C2×C4⋊C4×C149C2211yescharacteristic
20#106×C149—22no—
21C2×Dic298—21no—
22C2×Dic298—21no—
23C2×Dic298—21no—
24C2×Dic298—21no—
25C2×Dic298—21no—
26C2×Dic298Q812yes—
27C22×Dic149—21no—
28C22×Dic149—21no—
29C22×Dic149D412yes—
30C2×#11924746—21no—
31C2×#11924746—21no—
32C2×#11924746D412yes—
33C4⋊Dic149—21no—
34C4⋊Dic149—21no—
35#14558715—44no—
36C4×Dic149—21no—
37C4×Dic149—21no—
38C22×C4×C149—21no—
39C22×C4×C149—21no—
40C22×C4×C149C2311yescharacteristic
41C2×C8×C149—21no—
42C2×C8×C149—21no—
43C2×C8×C149D412yes—
44C4⋊C4×C149—21no—
45C4⋊C4×C149—21no—
46C4⋊C4×C149—21no—
47C4⋊C4×C149—21no—
48Dic298—22no—
49Dic298—22no—
50Dic298—41no—
51Dic298—41no—
52C2×Dic149—22no—
53C2×Dic149—22no—
54C2×Dic149—22no—
55C2×Dic149—41no—
56C2×Dic149—41no—
57C2×Dic149—41no—
58C2×Dic149—42no—
59C2×Dic149SD1614yes—
60#11924746—22no—
61C23×C149C2×D411yescharacteristic
62C2×C4×C149—41no—
63C2×C4×C149—41no—
64C2×C4×C149—42no—
65C2×C4×C149—42no—
66C2×C4×C149C2×D411yescharacteristic
67C2×C4×C149C2×D411yescharacteristic
68C2×C4×C149C2×Q811yescharacteristic
69C2×C4×C149#4111yescharacteristic
70C2×C4×C149#4111yescharacteristic
71C2×C4×C149#4111yescharacteristic
72C8×C149—22no—
73C22×C149C22⋊Q811yescharacteristic
74C22×C149#12311yescharacteristic
75C22×C149#12711yescharacteristic
76C22×C149C2×SD1612yes—
77C22×C149#13712yes—
78C4×C149—81no—
79C4×C149—81no—
80C4×C149C22⋊Q811yescharacteristic
81C4×C149C22⋊Q811yescharacteristic
82C4×C149#12311yescharacteristic
83C4×C149#12311yescharacteristic
84Dic149—24no—
85Dic149—42no—
86Dic149—81no—
87C2×C149#39911yescharacteristic
88C2×C149#47512yes—
89C2×C149#48312yes—
90C2×C149#49211yescharacteristic
91C2×C149#49711yescharacteristic
92C149#209611yescharacteristic, complemented, Sylow
93#2096—1491nomaximal, Sylow
94C2×#106—1491no—
95C2×#106D14911yescharacteristic
96C2×#103—1491no—
97C2×#103—1491no—
98#391—1491no—
99#384—1491no—
100#336—1491no—
101C22×Q8—1491no—
102C22×C8—1491no—
103C22×C8C2×D14911yescharacteristic
104C2×C4⋊C4—2982no—
105C2×C4⋊C4—1491no—
106C2×C4⋊C4C2×D14911yescharacteristic
107C2×C4⋊C4C2×D14911yescharacteristic
108C2×C42—1491no—
109#106—22no—
110#106—2982no—
111#103—2982no—
112#103—2982no—
113#95—2982no—
114C2×Q8—2981no—
115C2×Q8—2981no—
116C2×Q8—2981no—
117C2×Q8—2981no—
118C2×Q8—2981no—
119C2×Q8—1492no—
120C22×C4—21no—
121C22×C4—21no—
122C22×C4—2981no—
123C22×C4—2981no—
124C22×C4—1492no—
125C22×C4C22×D14911yescharacteristic
126C2×C8—21no—
127C2×C8—21no—
128C2×C8—2981no—
129C2×C8—2981no—
130C2×C8—1492no—
131C2×C8C22⋊D14912yes—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—21no—
135C4⋊C4—21no—
136C4⋊C4—2981no—
137C4⋊C4—2981no—
138C4⋊C4—5964no—
139C42—2981no—
140C42—2981no—
141C23D4×D14911yescharacteristic
142Q8—2982no—
143Q8—2982no—
144Q8—5961no—
145Q8—5961no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—42no—
149C2×C4—42no—
150C2×C4—2982no—
151C2×C4—2982no—
152C2×C4—2982no—
153C2×C4—5961no—
154C2×C4—5961no—
155C2×C4—5961no—
156C2×C4—5962no—
157C2×C4—1494no—
158C2×C4D4×D14911yescharacteristic
159C2×C4C2×C22⋊D14911yescharacteristic
160C2×C4Q8×D14911yescharacteristic
161C2×C4#1455873611yescharacteristic
162C2×C4#1455873611yescharacteristic
163C2×C4#1455873711yescharacteristic
164C8—22no—
165C8—2982no—
166C22#1801188911yescharacteristic
167C22#1801189611yescharacteristic
168C22#1801190711yescharacteristic
169C22SD16×D14912yes—
170C22#1801194012yes—
171C4—81no—
172C4—81no—
173C4—2984no—
174C4—5962no—
175C4—11921no—
176C4#1801188711yescharacteristic
177C4#1801188911yescharacteristic
178C4#1801189411yescharacteristic
179C4#1801189611yescharacteristic
180C2#2374956011yescharacteristic
181C2#2374990912yes—
182C2#2374995712yes—
183C2#2374999611yescharacteristic
184C2#2375001611yescharacteristic
subgroupG/H
centerC23D4×D149
commutator, cosocleC22×C4×C149C23
FrattiniC22×C4C22×D149
FittingC2×#106×C149C2
socle, prime radicalC23×C149C2×D4
hypercenterC2×#106D149
hypocenterC149#2096
LCSG ▷ C22×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
92. C149#2096semidirect

Maximal subgroups

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

subgroupindex
C2×#180118422
C2×#180118362
C2×#180118342
#237495302
#237494942
#237493792
C2×#106×C1492
#2096149