Finite Group Databasebeta

← #34060597

Subgroups — #34060597

Order 19072.

306 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 70 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
1#23750596C211yesmaximal, characteristic
2C4×C22⋊#10597010C211yesmaximal, characteristic
3#23750495C214yesmaximal, complemented
4C2×#18011869C211yesmaximal, characteristic
5C2×#14558746C2212yes—
6C2×C22⋊#10597010—21no—
7C2×C4×#10597010C2212yes—
8#18011968—21no—
9C22⋊#11924753—21no—
10(C2×#10597010)⋊C4—21no—
11C22×C4×D149C2211yescharacteristic
12#18011869—21no—
13#18011869—21no—
14#18011869C412yescomplemented
15#18011869C2212yes—
16C2×C4⋊Dic149C411yescharacteristic, complemented
17C2×#14558713—21no—
18C2×C4×Dic149—21no—
19C2×C4⋊C4×C149C411yescharacteristic, complemented
20C22×#10597010—22no—
21#14558746—24no—
22C2×#11924753—22no—
23C22⋊#10597010—24no—
24C4×#10597010—24no—
25C23×D149D411yescharacteristic
26C22×Dic149—21no—
27C22×Dic149D411yescharacteristic
28C2×C4×D149—24no—
29C2×C4×D149C2×C411yescharacteristic
30C2×C4×D149D411yescharacteristic
31C2×C4×D149D411yescharacteristic
32C2×C4×D149C2311yescharacteristic
33C4⋊Dic149—21no—
34C4⋊Dic149C2×C412yes—
35#14558713—22no—
36#14558713—22no—
37C4×Dic149—22no—
38C4×Dic149—22no—
39C22×C4×C149—21no—
40C22×C4×C149C2×C411yescharacteristic
41C4⋊C4×C149—21no—
42C4⋊C4×C149C2×C412yes—
43C2×#10597010—24no—
44C2×#10597010—42no—
45C2×#10597010—42no—
46#11924753—42no—
47C22×D149—22no—
48C22×D149—22no—
49C22×D149—41no—
50C22×D149C22⋊C411yescharacteristic
51C22×D149C2×D411yescharacteristic
52C2×Dic149—22no—
53C2×Dic149—22no—
54C2×Dic149—42no—
55C2×Dic149C22⋊C411yescharacteristic
56C2×Dic149C2×D411yescharacteristic
57C4×D149—22no—
58C4×D149—22no—
59C4×D149—22no—
60C4×D149#4114yes—
61C23×C149C22⋊C411yescharacteristic
62C2×C4×C149—22no—
63C2×C4×C149—22no—
64C2×C4×C149—42no—
65C2×C4×C149C22⋊C411yescharacteristic
66C2×C4×C149C22×C411yescharacteristic
67C22×C149—21no—
68C22×C149—21no—
69C22×C149#10412yes—
70C22×C149C2×C22⋊C411yescharacteristic
71C2×D149—21no—
72C2×D149—21no—
73C2×D149—21no—
74C2×D149—21no—
75C2×D149—21no—
76C2×D149—44no—
77C2×D149#12312yes—
78#10597010—44no—
79C4×C149—21no—
80C4×C149—42no—
81C4×C149#11712yes—
82Dic149—21no—
83Dic149—42no—
84Dic149#12312yes—
85C2×C149—22no—
86C2×C149#38111yescharacteristic
87C2×C149C2×#10411yescharacteristic
88C2×C149#42111yescharacteristic
89D149—22no—
90D149—41no—
91C149#182611yescharacteristic, complemented, Sylow
92#1826—1491nomaximal, Sylow
93C2×#117—1491no—
94#407—1491no—
95C4×C22⋊C4—1491no—
96#339—1494no—
97C23×C4—1491no—
98C2×M16—1492no—
99#117—2981no—
100#117—2981no—
101#117—1492no—
102#117—1492no—
103C2×C4⋊C4—1491no—
104C2×C4⋊C4#1059701011yescharacteristic, complemented
105C2×C22⋊C4—2981no—
106C2×C22⋊C4—2981no—
107C2×C42—2981no—
108C2×C42—1492no—
109C22⋊C8—2981no—
110C22⋊C8—2981no—
111#95—2981no—
112C24—1491no—
113C22×C4—21no—
114C22×C4—2984no—
115C22×C4—2982no—
116C22×C4—2981no—
117C22×C4—1491no—
118C22×C4—1491no—
119C22×C4—1491no—
120C22×C4—1491no—
121C22×C4—1491no—
122C22×C4C2×#1059701011yescharacteristic
123M16—2984no—
124C2×C8—2982no—
125C4⋊C4—21no—
126C4⋊C4—2981no—
127C4⋊C4—1492no—
128C4⋊C4C2×#1059701012yes—
129C22⋊C4—2982no—
130C22⋊C4—2982no—
131C22⋊C4—2984no—
132C42—2982no—
133C42—2982no—
134C42—2984no—
135C23—2982no—
136C23—2982no—
137C23—5961no—
138C23—1491no—
139C23—1491no—
140C23C22⋊#1059701011yescharacteristic
141C2×C4—22no—
142C2×C4—22no—
143C2×C4—42no—
144C2×C4—2982no—
145C2×C4—2982no—
146C2×C4—2982no—
147C2×C4—2982no—
148C2×C4—2984no—
149C2×C4—2982no—
150C2×C4—5962no—
151C2×C4—5962no—
152C2×C4—5962no—
153C2×C4—1491no—
154C2×C4—1491no—
155C2×C4—1494no—
156C2×C4C22⋊#1059701011yescharacteristic
157C2×C4C22×#1059701011yescharacteristic
158C8—5962no—
159C22—21no—
160C22—21no—
161C22—2981no—
162C22—2981no—
163C22—2981no—
164C22—2981no—
165C22—2981no—
166C22—5964no—
167C22—1492no—
168C22#1801197512yes—
169C22C2×C22⋊#1059701011yescharacteristic
170C4—21no—
171C4—42no—
172C4—2981no—
173C4—5964no—
174C4—5962no—
175C4—1492no—
176C4#1801199012yes—
177C2—22no—
178C2—2982no—
179C2—5961no—
180C2#2375056811yescharacteristic
181C2C2×#1801197511yescharacteristic
182C2#2375062411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC2×C4⋊C4×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC23×D149D4
cosocleC2×C4×D149C23
hypercenterC2×C4⋊C4#10597010
hypocenterC149#1826
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #23750495C2semidirect
14. #18011869C4semidirect
16. C2×C4⋊Dic149C4semidirect
19. C2×C4⋊C4×C149C4semidirect
91. C149#1826semidirect
104. C2×C4⋊C4#10597010semidirect

Maximal subgroups

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

subgroupindex
#237505962
C4×C22⋊#105970102
#237504952
C2×#180118692
#1826149