Finite Group Databasebeta

← D8×D596 #34056367

Subgroups — D8×D596 #34056367

Order 19072.

620 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 141 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×D8×D149C212yesmaximal, complemented
2D4×D596C212yesmaximal, complemented
3#23750002C211yesmaximal, characteristic, complemented
4#23749862C212yesmaximal, complemented
5#23749820C212yesmaximal, complemented
6#23749760C214yesmaximal, complemented
7C8×D596C211yesmaximal, characteristic, complemented
8C4×D8×C149C211yesmaximal, characteristic, complemented
9C22×D596—22no—
10C2×D4×D149C2214yescomplemented
11C2×D1192C2212yescomplemented
12C2×D1192C2212yescomplemented
13C2×#14558721C2214yescomplemented
14D8×D149—28no—
15C2×C8×D149C2212yescomplemented
16#18011908C2212yescomplemented
17#18011886C2214yescomplemented
18#18011885—22no—
19#18011881—24no—
20C4×D596C2211yescharacteristic
21C4⋊#11924746C2211yescharacteristic, complemented
22#18011831C2214yescomplemented
23#18011823C2212yescomplemented
24C2×D8×C149C2211yescharacteristic
25C4×D4×C149C2212yescomplemented
26#107×C149C2211yescharacteristic, complemented
27#102×C149C2212yescomplemented
28C4×C8×C149C2211yescharacteristic, complemented
29C23×D149—24no—
30C2×D596—24no—
31C2×D596—22no—
32C2×D596—22no—
33C2×D596—48no—
34C2×D596D411yescharacteristic
35C2×D596C2314yes—
36C2×C22⋊D149—24no—
37D4×D149—28no—
38D4×D149—44no—
39C2×C4×D149C2312yes—
40D1192—24no—
41D1192—42no—
42#14558721—28no—
43C2×#11924746C2312yes—
44C8×D149—24no—
45C4⋊Dic149D411yescharacteristic
46#14558713—24no—
47#14558713D412yes—
48C2×D4×C149C2312yes—
49C22×C4×C149—22no—
50D8×C149D414yescomplemented
51C2×C8×C149C2311yescharacteristic
52C2×C8×C149C2311yescharacteristic
53C4⋊C4×C149C2312yes—
54C22⋊C4×C149—22no—
55C42×C149C2311yescharacteristic
56C22×D149—24no—
57C22×D149—48no—
58C22×D149—48no—
59C22×D149—84no—
60C22×D149C2×D412yes—
61D596—24no—
62D596—24no—
63D596—48no—
64D596—44no—
65D596—82no—
66D596D814yesdirect product factor
67C22⋊D149—48no—
68C2×Dic149C2×D412yes—
69C4×D149—22no—
70C4×D149—22no—
71#11924746—22no—
72C23×C149—22no—
73D4×C149—22no—
74D4×C149C2×D414yescomplemented
75C2×C4×C149—22no—
76C2×C4×C149—44no—
77C2×C4×C149C2×D411yescharacteristic
78C2×C4×C149C2×D411yescharacteristic
79C2×C4×C149C2411yescharacteristic
80C8×C149—21no—
81C8×C149C2×D412yescomplemented
82C22×C149—24no—
83C22×C149—42no—
84C22×C149—42no—
85C22×C149C22×D411yescharacteristic
86C2×D149—22no—
87C2×D149—22no—
88C2×D149—44no—
89C2×D149—44no—
90C2×D149—44no—
91C2×D149—816no—
92C2×D149C2×D814yescomplemented
93C4×C149—21no—
94C4×C149—42no—
95C4×C149C2×D812yescomplemented
96C4×C149C22×D411yescharacteristic
97C4×C149H(5,𝔽2)11yescharacteristic
98Dic149—22no—
99C2×C149—44no—
100C2×C149D4211yescharacteristic
101C2×C149C22×D811yescharacteristic
102C2×C149#57611yescharacteristic
103D149—24no—
104D149—84no—
105C149D4×D811yescharacteristic, complemented, Sylow
106D4×D8—1491nomaximal, Sylow
107C22×D8—1492no—
108D42—1492no—
109#493—1491no—
110#466—1492no—
111#459—1492no—
112#447—1494no—
113C4×D8D14911yescharacteristic, complemented
114C8×D4—1491no—
115C22×D4—2982no—
116C22×D4—1494no—
117C2×D8—2988no—
118C2×D8—1494no—
119C2×D8—1492no—
120C2×D8—1492no—
121C2×D8C2×D14911yescharacteristic
122C22×C8—1492no—
123#127—1492no—
124#121—2982no—
125#121—1494no—
126#120—2984no—
127C4×D4—1491no—
128C4×D4C2×D14912yescomplemented
129#107C2×D14911yescharacteristic, complemented
130C4⋊C8—1491no—
131#102—1494no—
132#102C2×D14912yescomplemented
133C22⋊C8—1492no—
134C4×C8C2×D14911yescharacteristic, complemented
135C24—2984no—
136C2×D4—2984no—
137C2×D4—2988no—
138C2×D4—2984no—
139C2×D4—2982no—
140C2×D4—2982no—
141C2×D4—5968no—
142C2×D4—5964no—
143C2×D4—1491no—
144C2×D4—1494no—
145C2×D4C22×D14912yes—
146C22×C4—22no—
147C22×C4—1492no—
148D8—2988no—
149D8—2984no—
150D8—5962no—
151D8D59614yesdirect product factor
152C2×C8—2984no—
153C2×C8—1492no—
154C2×C8C22×D14911yescharacteristic
155C2×C8C22×D14911yescharacteristic
156C4⋊C4—1491no—
157C4⋊C4C22×D14912yes—
158C22⋊C4—22no—
159C22⋊C4—2984no—
160C22⋊C4—1492no—
161C42C22×D14911yescharacteristic
162C23—22no—
163C23—2984no—
164C23—5968no—
165C23—5968no—
166C23—1492no—
167C23—11924no—
168D4—22no—
169D4—2984no—
170D4—2984no—
171D4—5968no—
172D4—5968no—
173D4—5964no—
174D4—1494no—
175D4—11922no—
176D4C2×D59614yescomplemented
177C2×C4—22no—
178C2×C4—44no—
179C2×C4—2982no—
180C2×C4—2982no—
181C2×C4—1492no—
182C2×C4D4×D14911yescharacteristic
183C2×C4D4×D14911yescharacteristic
184C2×C4C23×D14911yescharacteristic
185C8—21no—
186C8—2982no—
187C8C2×D59612yescomplemented
188C22—24no—
189C22—42no—
190C22—42no—
191C22—2982no—
192C22—2982no—
193C22—5964no—
194C22—5964no—
195C22—5964no—
196C22—1494no—
197C22—119216no—
198C22C2×D4×D14911yescharacteristic
199C4—21no—
200C4—42no—
201C4—2982no—
202C4D8×D14912yescomplemented
203C4C22×D59611yescharacteristic
204C4#1801195711yescharacteristic
205C2—44no—
206C2—2984no—
207C2—11924no—
208C2D4×D59611yescharacteristic
209C2C2×D8×D14911yescharacteristic
210C2#2375042711yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC4×D8×C149C2
socleC22×C149C22×D4
hypercenterC4×D8D149
hypocenterC149D4×D8
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. C2×D8×D149C2semidirect
2. D4×D596C2semidirect
3. #23750002C2semidirect
4. #23749862C2semidirect
5. #23749820C2semidirect
6. #23749760C2semidirect
7. C8×D596C2semidirect
8. C4×D8×C149C2semidirect
10. C2×D4×D149C22semidirect
11. C2×D1192C22semidirect
12. C2×D1192C22semidirect
13. C2×#14558721C22semidirect
15. C2×C8×D149C22semidirect
16. #18011908C22semidirect
17. #18011886C22semidirect
21. C4⋊#11924746C22semidirect
22. #18011831C22semidirect
23. #18011823C22semidirect
25. C4×D4×C149C22semidirect
26. #107×C149C22semidirect
27. #102×C149C22semidirect
28. C4×C8×C149C22semidirect
50. D8×C149D4semidirect
66. D596D8direct (N × H)
74. D4×C149C2×D4semidirect
81. C8×C149C2×D4semidirect
92. C2×D149C2×D8semidirect
95. C4×C149C2×D8semidirect
105. C149D4×D8semidirect
113. C4×D8D149semidirect
128. C4×D4C2×D149semidirect
129. #107C2×D149semidirect
132. #102C2×D149semidirect
134. C4×C8C2×D149semidirect
151. D8D596direct (N × H)
176. D4C2×D596semidirect
187. C8C2×D596semidirect
202. C4D8×D149semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D1492
D4×D5962
#237500022
#237498622
#237498202
#237497602
C8×D5962
C4×D8×C1492
D4×D8149