Finite Group Databasebeta

← C2×#23750473 #34059978

Subgroups — C2×#23750473 #34059978

Order 19072.

344 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 106 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×C4⋊#11924753C211yesmaximal, characteristic, complemented
2C2×C4×#11924753C211yesmaximal, characteristic, complemented
3#23750473C214yesmaximal, direct product factor
4C2×#18011873C211yesmaximal, characteristic
5C22×#11924753—21no—
6C22×#11924753—21no—
7C4⋊#11924753—21no—
8C4⋊#11924753C2212yescomplemented
9C4×#11924753—21no—
10C4×#11924753C2212yescomplemented
11C22×D596C411yescharacteristic
12C22×C4×D149—21no—
13#18011873—21no—
14#18011873—21no—
15#18011873C412yes—
16#18011873C2212yes—
17C2×#14558713—21no—
18C2×C4×Dic149C2211yescharacteristic
19C2×C4⋊C4×C149C411yescharacteristic
20C2×#11924753—24no—
21C2×#11924753—22no—
22C2×#11924753—22no—
23C2×#11924753—42no—
24C23×D149—21no—
25C2×D596—21no—
26C2×D596—22no—
27C2×D596C814yescomplemented
28C2×D596C2×C412yes—
29C22×Dic149D411yescharacteristic
30C22×Dic149D411yescharacteristic
31C2×C4×D149—22no—
32C2×C4×D149—22no—
33C2×C4×D149—42no—
34C2×C4×D149—42no—
35#14558713—22no—
36#14558713—22no—
37C4×Dic149C2×C411yescharacteristic
38C4×Dic149D411yescharacteristic
39C4×Dic149D411yescharacteristic
40C4×Dic149C2311yescharacteristic
41C22×C4×C149—21no—
42C22×C4×C149C2×C411yescharacteristic
43C4⋊C4×C149—21no—
44C4⋊C4×C149C2×C412yes—
45#11924753—24no—
46#11924753—42no—
47C22×D149—24no—
48C22×D149—22no—
49C22×D149—42no—
50C22×D149—42no—
51D596—24no—
52D596—22no—
53D596C2×C814yescomplemented
54C2×Dic149—22no—
55C2×Dic149C22⋊C411yescharacteristic
56C2×Dic149C22⋊C411yescharacteristic
57C2×Dic149D812yes—
58C2×Dic149SD1612yes—
59C2×Dic149C2×D411yescharacteristic
60C2×Dic149C2×D411yescharacteristic
61C4×D149—44no—
62C4×D149—42no—
63C4×D149—42no—
64C23×C149C22⋊C411yescharacteristic
65C2×C4×C149—22no—
66C2×C4×C149—42no—
67C2×C4×C149C22⋊C411yescharacteristic
68C2×C4×C149C2×C812yes—
69C2×C4×C149M1612yes—
70C2×C4×C149C22×C411yescharacteristic
71C22×C149C22⋊C812yes—
72C22×C149#10212yes—
73C22×C149#10412yes—
74C22×C149C2×C22⋊C411yescharacteristic
75C2×D149—24no—
76C2×D149—48no—
77C2×D149—42no—
78C2×D149—42no—
79C4×C149—42no—
80C4×C149C22⋊C812yes—
81C4×C149C22×C811yescharacteristic
82C4×C149C2×M1611yescharacteristic
83Dic149—21no—
84Dic149—21no—
85Dic149#10212yes—
86Dic149C2×D811yescharacteristic
87Dic149C2×SD1611yescharacteristic
88C2×C149D4⋊C814yescomplemented
89C2×C149C2×C22⋊C811yescharacteristic
90C2×C149C2×#10211yescharacteristic
91C2×C149C2×#10411yescharacteristic
92D149—44no—
93C149C2×D4⋊C811yescharacteristic, complemented, Sylow
94C2×D4⋊C8—1491nomaximal, Sylow
95C2×C4×D4—1491no—
96C2×C4⋊C8—1491no—
97C2×C4×C8—1491no—
98D4⋊C8—1494no—
99C22×D4—1491no—
100C23×C4—2981no—
101C22×C8—2981no—
102C22×C8—2981no—
103C4×D4—2981no—
104C4×D4—2981no—
105C4×D4—1492no—
106C4×D4—1492no—
107C2×C4⋊C4#1059701011yescharacteristic
108C2×C22⋊C4—2981no—
109C2×C42—1491no—
110C4⋊C8—2981no—
111C4⋊C8—1492no—
112C4×C8—2981no—
113C4×C8—1492no—
114C24—2981no—
115C2×D4—2981no—
116C2×D4—2982no—
117C2×D4—1494no—
118C2×D4—1492no—
119C22×C4—21no—
120C22×C4—2982no—
121C22×C4—2982no—
122C22×C4—5962no—
123C22×C4—5962no—
124C22×C4—1491no—
125C22×C4—1491no—
126C22×C4C2×#1059701011yescharacteristic
127C2×C8—2984no—
128C2×C8—2982no—
129C2×C8—2982no—
130C2×C8—5962no—
131C4⋊C4—21no—
132C4⋊C4C2×#1059701012yes—
133C22⋊C4—2982no—
134C22⋊C4—2982no—
135C42—1491no—
136C42—1491no—
137C42—1491no—
138C42—1491no—
139C23—2984no—
140C23—2982no—
141C23—5962no—
142C23—5962no—
143C23C22⋊#1059701011yescharacteristic
144D4—2984no—
145D4—2982no—
146D4—1494no—
147C2×C4—22no—
148C2×C4—42no—
149C2×C4—2982no—
150C2×C4—5962no—
151C2×C4—5964no—
152C2×C4—5962no—
153C2×C4—1491no—
154C2×C4—1491no—
155C2×C4—1492no—
156C2×C4—1492no—
157C2×C4—1491no—
158C2×C4—1491no—
159C2×C4C22⋊#1059701011yescharacteristic
160C2×C4D149⋊C812yes—
161C2×C4#1455874612yes—
162C2×C4C22×#1059701011yescharacteristic
163C8—2984no—
164C8—5962no—
165C22—2984no—
166C22—5968no—
167C22—5962no—
168C22—5962no—
169C22#1801196812yes—
170C22#1801197312yes—
171C22#1801197612yes—
172C22C2×C22⋊#1059701011yescharacteristic
173C4—42no—
174C4—2981no—
175C4—2981no—
176C4—1491no—
177C4—1492no—
178C4—1491no—
179C4#1801196812yes—
180C4C2×D149⋊C811yescharacteristic
181C4C2×#1455874611yescharacteristic
182C2—5964no—
183C2#2375047314yesdirect product factor
184C2C2×#1801196811yescharacteristic
185C2C2×#1801197311yescharacteristic
186C2C2×#1801197611yescharacteristic
subgroupG/H
centerC23C22⋊#10597010
commutatorC4×C149C22×C8
FrattiniC2×C4C22×#10597010
FittingC2×C4⋊C4×C149C4
socleC23×C149C22⋊C4
prime radicalC22×D596C4
cosocleC4×Dic149C23
hypercenterC2×C4⋊C4#10597010
hypocenterC149C2×D4⋊C8
LCSG ▷ C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊#11924753C2semidirect
2. C2×C4×#11924753C2semidirect
3. #23750473C2direct (N × H)
8. C4⋊#11924753C22semidirect
10. C4×#11924753C22semidirect
27. C2×D596C8semidirect
53. D596C2×C8semidirect
88. C2×C149D4⋊C8semidirect
93. C149C2×D4⋊C8semidirect
183. C2#23750473direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4⋊#119247532
C2×C4×#119247532
#237504732
C2×#180118732
C2×D4⋊C8149