Finite Group Databasebeta

← C2×#23750059 #34057812

Subgroups — C2×#23750059 #34057812

Order 19072.

400 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 117 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×#18011930C211yesmaximal, characteristic, complemented
2C2×D8×D149C211yesmaximal, characteristic, complemented
3#23750059C218yesmaximal, direct product factor
4C2×#18011856C211yesmaximal, characteristic, complemented
5C2×#18011855C211yesmaximal, characteristic, complemented
6C2×#18011852C211yesmaximal, characteristic, complemented
7C2×#18011850C211yesmaximal, characteristic, complemented
8C2×D16×C149C211yesmaximal, characteristic, complemented
9C2×#14558735—21no—
10C2×D4×D149—21no—
11#18011930—22no—
12#18011930C2214yescomplemented
13C2×Dic596C2211yescharacteristic, complemented
14C2×#14558724—21no—
15C2×D1192C2211yescharacteristic
16C2×#14558721—21no—
17D8×D149—22no—
18D8×D149C2214yescomplemented
19C2×C8×D149C2211yescharacteristic
20#18011856C2214yescomplemented
21#18011855C2214yescomplemented
22#18011852C2214yescomplemented
23#18011850C2214yescomplemented
24C2×#14558711C2211yescharacteristic, complemented
25C2×D8×C149C2211yescharacteristic
26C2×D8×C149C2211yescharacteristic, complemented
27D16×C149C2214yescomplemented
28C2×C16×C149C2211yescharacteristic, complemented
29C23×D149—41no—
30#14558735—24no—
31#14558735—42no—
32C2×Dic298—21no—
33C2×D596—21no—
34C2×C22⋊D149—41no—
35C2×C22⋊D149—41no—
36D4×D149—24no—
37D4×D149—42no—
38C22×Dic149—41no—
39C2×C4×D149D411yescharacteristic
40Dic596—21no—
41Dic596C2312yescomplemented
42#14558724—24no—
43D1192—21no—
44D1192C2312yes—
45#14558721—24no—
46C2×#11924746D411yescharacteristic
47C8×D149D412yes—
48C8×D149C2312yes—
49#14558711C2312yescomplemented
50C2×D4×C149—21no—
51C2×D4×C149—21no—
52D8×C149—21no—
53D8×C149—21no—
54D8×C149C2312yes—
55D8×C149C2312yescomplemented
56C2×C8×C149C2311yescharacteristic
57C16×C149C2312yescomplemented
58C22×D149—41no—
59C22×D149—44no—
60C22×D149—84no—
61C22×D149D811yescharacteristic
62Dic298—22no—
63Dic298—41no—
64D596—22no—
65D596—41no—
66C22⋊D149—44no—
67C22⋊D149—44no—
68C2×Dic149—41no—
69C2×Dic149—44no—
70C2×Dic149D811yescharacteristic
71C4×D149D812yes—
72C4×D149C2×D412yes—
73#11924746C2×D412yes—
74C23×C149—41no—
75C23×C149—41no—
76D4×C149—22no—
77D4×C149—22no—
78D4×C149—41no—
79D4×C149—41no—
80C2×C4×C149C2×D411yescharacteristic
81C8×C149C2×D411yescharacteristic
82C8×C149C2411yescharacteristic
83C22×C149—42no—
84C22×C149—42no—
85C22×C149—82no—
86C22×C149—82no—
87C22×C149C2×D811yescharacteristic
88C2×D149—22no—
89C2×D149—42no—
90C2×D149—88no—
91C2×D149—82no—
92C2×D149C2×D812yes—
93C4×C149C2×D811yescharacteristic
94C4×C149C22×D411yescharacteristic
95Dic149—42no—
96Dic149C2×D812yes—
97C2×C149—82no—
98C2×C149—82no—
99C2×C149#50912yescomplemented
100C2×C149C22×D811yescharacteristic
101D149—22no—
102D149—82no—
103C149C2×#50911yescharacteristic, complemented, Sylow
104C2×#509—1491nomaximal, Sylow
105C2×#135—1491no—
106C22×D8—1491no—
107#509—1498no—
108C2×SD32—1491no—
109C2×SD32—1491no—
110C2×D16—1491no—
111C2×D16D14911yescharacteristic, complemented
112C2×M32—1491no—
113C2×#41—2981no—
114C22×D4—2981no—
115#135—2982no—
116#135—1494no—
117C2×Q16—1491no—
118C2×SD16—2981no—
119C2×D8—2982no—
120C2×D8—2981no—
121C2×D8—1494no—
122C2×D8—1491no—
123C2×D8C2×D14911yescharacteristic
124C2×D8C2×D14911yescharacteristic, complemented
125C22×C8—1491no—
126SD32—1494no—
127SD32—1494no—
128D16—1494no—
129D16C2×D14914yescomplemented
130M32—1494no—
131C2×C16—1491no—
132C2×C16C2×D14911yescharacteristic, complemented
133C24—5961no—
134#41—2984no—
135#41—5962no—
136C2×Q8—2981no—
137C2×D4—21no—
138C2×D4—21no—
139C2×D4—2984no—
140C2×D4—2981no—
141C2×D4—5961no—
142C2×D4—5962no—
143C2×D4—5961no—
144C22×C4—5961no—
145C22×C4—1491no—
146Q16—2981no—
147Q16—1492no—
148SD16—2984no—
149D8—21no—
150D8—21no—
151D8—2984no—
152D8—2981no—
153D8—1492no—
154D8C22×D14912yes—
155D8C22×D14912yescomplemented
156C2×C8—1491no—
157C2×C8—1492no—
158C2×C8—1492no—
159C2×C8C22×D14911yescharacteristic
160C16—1492no—
161C16C22×D14912yescomplemented
162C23—41no—
163C23—41no—
164C23—5964no—
165C23—5961no—
166C23—1491no—
167C23—11924no—
168Q8—2982no—
169Q8—5961no—
170D4—22no—
171D4—22no—
172D4—41no—
173D4—41no—
174D4—2982no—
175D4—5964no—
176D4—5964no—
177D4—5961no—
178C2×C4—5961no—
179C2×C4—5964no—
180C2×C4—1491no—
181C2×C4—1492no—
182C2×C4—1492no—
183C2×C4D4×D14911yescharacteristic
184C8—1492no—
185C8D4×D14911yescharacteristic
186C8C23×D14911yescharacteristic
187C22—42no—
188C22—42no—
189C22—82no—
190C22—82no—
191C22—2982no—
192C22—5962no—
193C22—1492no—
194C22—11928no—
195C22—11922no—
196C22D8×D14911yescharacteristic
197C4—5962no—
198C4—1492no—
199C4D8×D14911yescharacteristic
200C4C2×D4×D14911yescharacteristic
201C2—82no—
202C2—82no—
203C2—2982no—
204C2—11922no—
205C2#2375005912yesdirect product factor
206C2C2×D8×D14911yescharacteristic
subgroupG/H
centerC22D8×D149
commutator, cosocleC8×C149C24
FrattiniC8C23×D149
FittingC2×D16×C149C2
socleC22×C149C2×D8
hypercenterC2×D16D149
hypocenterC149C2×#509
LCSG ▷ C8×C149 ▷ C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×D16

Complements

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

NH ≅ G/Ntype
1. C2×#18011930C2semidirect
2. C2×D8×D149C2semidirect
3. #23750059C2direct (N × H)
4. C2×#18011856C2semidirect
5. C2×#18011855C2semidirect
6. C2×#18011852C2semidirect
7. C2×#18011850C2semidirect
8. C2×D16×C149C2semidirect
12. #18011930C22semidirect
13. C2×Dic596C22semidirect
18. D8×D149C22semidirect
20. #18011856C22semidirect
21. #18011855C22semidirect
22. #18011852C22semidirect
23. #18011850C22semidirect
24. C2×#14558711C22semidirect
26. C2×D8×C149C22semidirect
27. D16×C149C22semidirect
28. C2×C16×C149C22semidirect
41. Dic596C23semidirect
49. #14558711C23semidirect
55. D8×C149C23semidirect
57. C16×C149C23semidirect
99. C2×C149#509semidirect
103. C149C2×#509semidirect
111. C2×D16D149semidirect
124. C2×D8C2×D149semidirect
129. D16C2×D149semidirect
132. C2×C16C2×D149semidirect
155. D8C22×D149semidirect
161. C16C22×D149semidirect
205. C2#23750059direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#180119302
C2×D8×D1492
#237500592
C2×#180118562
C2×#180118552
C2×#180118522
C2×#180118502
C2×D16×C1492
C2×#509149