Finite Group Databasebeta

← #34044608

Subgroups — #34044608

Order 19072.

612 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 612 conjugacy classes of subgroups — too many to draw. Only its 101 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
1C22×#14558736C211yesmaximal, characteristic
2C2×#18011825C214yesmaximal, complemented
3#23749488C211yesmaximal, characteristic, complemented
4#381×C149C211yesmaximal, characteristic, complemented
5C2×#14558736—22no—
6C2×#14558736—22no—
7C2×#14558736—28no—
8C22×Dic298C411yescharacteristic, complemented
9C22×D596C411yescharacteristic, complemented
10C22×C22⋊D149C2212yes—
11C22×C4×D149C412yescomplemented
12C2×C22⋊Dic149C2212yes—
13#18011825—28no—
14#18011818—22no—
15C23×C4×C149C2211yescharacteristic
16C2×C22⋊C4×C149C2212yes—
17#95×C149—22no—
18C23×D149C2×C412yes—
19#14558736—216no—
20#14558736—216no—
21C2×Dic298—24no—
22C2×Dic298—22no—
23C2×D596—24no—
24C2×D596—22no—
25C2×C22⋊D149—24no—
26C2×C22⋊D149—22no—
27C2×C22⋊D149—22no—
28C2×C22⋊D149D418yes—
29C22×Dic149—22no—
30C22×Dic149C2×C412yes—
31C2×C4×D149—24no—
32C2×C4×D149—24no—
33C2×C4×D149—24no—
34C22⋊Dic149—24no—
35C24×C149C2311yescharacteristic
36C22×C4×C149—24no—
37C22×C4×C149—22no—
38C22×C4×C149C2×C411yescharacteristic
39C22×C4×C149C2×C411yescharacteristic
40C22×C4×C149D412yes—
41C22×C4×C149D412yes—
42C22⋊C4×C149—24no—
43C22×D149—22no—
44C22×D149—22no—
45C22×D149—44no—
46C22×D149C22⋊C414yes—
47Dic298—28no—
48D596—28no—
49C22⋊D149—28no—
50C22⋊D149—28no—
51C2×Dic149—22no—
52C2×Dic149—22no—
53C2×Dic149—44no—
54C2×Dic149—42no—
55C2×Dic149C22⋊C414yes—
56C4×D149—216no—
57C23×C149—42no—
58C23×C149C22×C411yescharacteristic
59C23×C149C2×D414yes—
60C23×C149C2×D411yescharacteristic
61C23×C149C2×D411yescharacteristic
62C2×C4×C149—22no—
63C2×C4×C149—22no—
64C2×C4×C149—24no—
65C2×C4×C149—24no—
66C2×C4×C149—44no—
67C2×C4×C149—42no—
68C2×C4×C149C22⋊C412yes—
69C2×C4×C149C22⋊C412yes—
70C22×C149—22no—
71C22×C149—22no—
72C22×C149—22no—
73C22×C149—44no—
74C22×C149C2×C22⋊C412yes—
75C22×C149C2×C22⋊C411yescharacteristic
76C22×C149#12012yes—
77C22×C149#12012yes—
78C2×D149—24no—
79C2×D149—44no—
80C2×D149—44no—
81C2×D149—44no—
82C4×C149—22no—
83C4×C149—22no—
84C4×C149—82no—
85Dic149—24no—
86Dic149—82no—
87C2×C149—22no—
88C2×C149—22no—
89C2×C149—22no—
90C2×C149#37911yescharacteristic
91C2×C149#41012yes—
92D149—44no—
93C149#178211yescharacteristic, complemented, Sylow
94#1782—1491nomaximal, Sylow
95C22×#41—1491no—
96C2×#99—1494no—
97#381—1491no—
98#381D14911yescharacteristic, complemented
99C2×#41—2988no—
100C2×#41—2982no—
101C2×#41—2982no—
102C22×Q8—1491no—
103C22×D4—1492no—
104C22×D4—1491no—
105C23×C4—1492no—
106C23×C4C2×D14911yescharacteristic
107C2×C22⋊C4—1492no—
108C2×C22⋊C4C2×D14912yes—
109#99—2988no—
110#95—22no—
111#95—2982no—
112C24—1492no—
113C24C22×D14911yescharacteristic
114#41—29816no—
115#41—29816no—
116C2×Q8—2984no—
117C2×Q8—2982no—
118C2×D4—2984no—
119C2×D4—2984no—
120C2×D4—2982no—
121C2×D4—2982no—
122C2×D4—2982no—
123C2×D4—1498no—
124C22×C4—24no—
125C22×C4—22no—
126C22×C4—2984no—
127C22×C4—2984no—
128C22×C4—2984no—
129C22×C4—2982no—
130C22×C4—1492no—
131C22×C4C4×D14911yescharacteristic
132C22×C4C4×D14911yescharacteristic
133C22×C4C22⋊D14912yes—
134C22×C4D59612yes—
135C22⋊C4—24no—
136C22⋊C4—2984no—
137C23—42no—
138C23—2982no—
139C23—2982no—
140C23—5964no—
141C23—1494no—
142C23C2×C4×D14911yescharacteristic
143C23D4×D14914yes—
144C23C2×C22⋊D14911yescharacteristic
145C23C2×D59611yescharacteristic
146Q8—2988no—
147D4—2988no—
148D4—2988no—
149D4—2988no—
150C2×C4—22no—
151C2×C4—22no—
152C2×C4—24no—
153C2×C4—24no—
154C2×C4—44no—
155C2×C4—42no—
156C2×C4—29816no—
157C2×C4—2982no—
158C2×C4—2982no—
159C2×C4—5964no—
160C2×C4—5962no—
161C2×C4—1494no—
162C2×C4#1455871312yes—
163C2×C4#1455871312yes—
164C22—22no—
165C22—22no—
166C22—22no—
167C22—44no—
168C22—2984no—
169C22—5964no—
170C22—5964no—
171C22—5964no—
172C22C22⋊C4×D14912yes—
173C22C2×#1455871311yescharacteristic
174C22#1801187912yes—
175C22#1801188112yes—
176C4—22no—
177C4—22no—
178C4—82no—
179C4—2984no—
180C4—11922no—
181C2—22no—
182C2—22no—
183C2—22no—
184C2—5964no—
185C2#2374948011yescharacteristic
186C2#2374959812yes—
subgroupG/H
centerC22C2×#14558713
commutatorC23×C149C22×C4
FrattiniC24C22×D149
Fitting#381×C149C2
socleC22×C149C2×C22⋊C4
prime radicalC22×#14558736C2
cosocleC24×C149C23
hypercenter#381D149
hypocenterC149#1782
LCSG ▷ C23×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C23×C4 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C2×#18011825C2semidirect
3. #23749488C2semidirect
4. #381×C149C2semidirect
8. C22×Dic298C4semidirect
9. C22×D596C4semidirect
11. C22×C4×D149C4semidirect
93. C149#1782semidirect
98. #381D149semidirect

Maximal subgroups

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

subgroupindex
C22×#145587362
C2×#180118252
#237494882
#381×C1492
#1782149