Finite Group Databasebeta

← #34056366

Subgroups — #34056366

Order 19072.

620 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 133 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
2#23750260C212yesmaximal, complemented
3#23749858C212yesmaximal, complemented
4#23749817C212yesmaximal, complemented
5#23749757C214yesmaximal, complemented
6C4×D1192C211yesmaximal, characteristic, complemented
7C8×D596C211yesmaximal, characteristic, complemented
8#493×C149C211yesmaximal, characteristic, complemented
9C2×D4×D149—22no—
10C2×D4×D149C2214yescomplemented
11C2×D1192C2211yescharacteristic
12C2×#14558721C2214yescomplemented
13D8×D149—28no—
14C2×C8×D149C2212yescomplemented
15#18011882—22no—
16#18011882C2214yescomplemented
17#18011879—24no—
18C4×D596C2211yescharacteristic
19C4×D596C2212yescomplemented
20#18011845C2211yescharacteristic, complemented
21C4⋊#11924746C2211yescharacteristic, complemented
22#18011833C2212yescomplemented
23#18011832C2214yescomplemented
24#18011823C2212yescomplemented
25C2×D8×C149C2212yescomplemented
26C2×D8×C149C2212yescomplemented
27#127×C149C2212yescomplemented
28C4×C8×C149C2211yescharacteristic, complemented
29C23×D149—24no—
30C2×D596D411yescharacteristic
31C2×D596C2312yes—
32C2×C22⋊D149—24no—
33C2×C22⋊D149—24no—
34D4×D149—28no—
35D4×D149—44no—
36D4×D149—48no—
37C2×C4×D149—22no—
38C2×C4×D149C2312yes—
39D1192D414yescomplemented
40#14558721—28no—
41C2×#11924746C2312yes—
42C8×D149—24no—
43C4⋊Dic149D411yescharacteristic
44C4⋊Dic149C2312yes—
45C22⋊Dic149—24no—
46#14558713—22no—
47#14558713D412yes—
48C2×D4×C149—22no—
49C2×D4×C149—22no—
50C2×D4×C149C2314yes—
51D8×C149—24no—
52D8×C149—42no—
53C2×C8×C149C2311yescharacteristic
54C2×C8×C149C2311yescharacteristic
55C42×C149C2311yescharacteristic
56C22×D149—22no—
57C22×D149—48no—
58C22×D149—48no—
59C22×D149—84no—
60C22×D149C2×D412yes—
61D596—22no—
62D596D814yescomplemented
63D596C2×D414yescomplemented
64C22⋊D149—48no—
65C22⋊D149—48no—
66C2×Dic149—22no—
67C2×Dic149C2×D412yes—
68C4×D149—22no—
69C4×D149—22no—
70C4×D149—44no—
71#11924746—22no—
72C23×C149—24no—
73D4×C149—24no—
74D4×C149—24no—
75D4×C149—44no—
76D4×C149—82no—
77C2×C4×C149C2×D411yescharacteristic
78C2×C4×C149C2×D411yescharacteristic
79C2×C4×C149C2411yescharacteristic
80C8×C149—21no—
81C8×C149C2×D412yescomplemented
82C22×C149—44no—
83C22×C149—44no—
84C22×C149—44no—
85C22×C149C22×D411yescharacteristic
86C2×D149—22no—
87C2×D149—22no—
88C2×D149—24no—
89C2×D149—42no—
90C2×D149—42no—
91C2×D149—816no—
92C2×D149C2×D814yescomplemented
93C4×C149—21no—
94C4×C149C2×D812yescomplemented
95C4×C149C22×D411yescharacteristic
96C4×C149H(5,𝔽2)11yescharacteristic
97Dic149—22no—
98Dic149—42no—
99C2×C149—84no—
100C2×C149D4211yescharacteristic
101C2×C149C22×D811yescharacteristic
102C2×C149#57611yescharacteristic
103D149—24no—
104D149—44no—
105C149D4×D811yescharacteristic, complemented, Sylow
106D4×D8—1491nomaximal, Sylow
107C22×D8—1492no—
108D42—1492no—
109#493D14911yescharacteristic, complemented
110#466—1492no—
111#459—1492no—
112#447—1494no—
113C4×D8—1491no—
114C8×D4—1491no—
115C22×D4—2982no—
116C22×D4—1494no—
117C2×D8—2988no—
118C2×D8—1494no—
119C2×D8—1491no—
120C2×D8C2×D14912yescomplemented
121C2×D8C2×D14912yescomplemented
122C22×C8—1492no—
123#127C2×D14912yescomplemented
124#121—2982no—
125#121—1494no—
126#120—2984no—
127C4×D4—1492no—
128C4×D4—1491no—
129#107—1491no—
130C4⋊C8—1491no—
131#102—1494no—
132#102—1492no—
133C22⋊C8—1492no—
134C4×C8C2×D14911yescharacteristic, complemented
135C24—2984no—
136C2×D4—22no—
137C2×D4—22no—
138C2×D4—2988no—
139C2×D4—2984no—
140C2×D4—2984no—
141C2×D4—5964no—
142C2×D4—5968no—
143C2×D4—1491no—
144C2×D4—1492no—
145C2×D4C22×D14914yes—
146C22×C4—2982no—
147C22×C4—1492no—
148D8—24no—
149D8—42no—
150D8—2988no—
151D8—1494no—
152C2×C8—2984no—
153C2×C8—1492no—
154C2×C8C22×D14911yescharacteristic
155C2×C8C22×D14911yescharacteristic
156C4⋊C4—1492no—
157C4⋊C4—1491no—
158C22⋊C4—2984no—
159C22⋊C4—2982no—
160C22⋊C4—1492no—
161C42C22×D14911yescharacteristic
162C23—24no—
163C23—2982no—
164C23—5968no—
165C23—5968no—
166C23—1492no—
167C23—11924no—
168D4—24no—
169D4—24no—
170D4—44no—
171D4—82no—
172D4—2982no—
173D4—5968no—
174D4—5968no—
175D4—1494no—
176D4—1494no—
177C2×C4—2982no—
178C2×C4—2982no—
179C2×C4—2982no—
180C2×C4—5964no—
181C2×C4—1492no—
182C2×C4D4×D14911yescharacteristic
183C2×C4D4×D14911yescharacteristic
184C2×C4C23×D14911yescharacteristic
185C8—21no—
186C8—2982no—
187C8D4×D14912yescomplemented
188C22—44no—
189C22—44no—
190C22—44no—
191C22—2982no—
192C22—2982no—
193C22—2984no—
194C22—5962no—
195C22—5962no—
196C22—1494no—
197C22—119216no—
198C22C2×D4×D14911yescharacteristic
199C4—21no—
200C4—2982no—
201C4—5962no—
202C4D8×D14912yescomplemented
203C4C2×D4×D14911yescharacteristic
204C4#1801195611yescharacteristic
205C2—84no—
206C2—2984no—
207C2—5964no—
208C2#2375026011yescharacteristic
209C2C2×D8×D14911yescharacteristic
210C2#2375042611yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#493×C149C2
socleC22×C149C22×D4
hypercenter#493D149
hypocenterC149D4×D8
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #493

Complements

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

NH ≅ G/Ntype
1. C2×D8×D149C2semidirect
2. #23750260C2semidirect
3. #23749858C2semidirect
4. #23749817C2semidirect
5. #23749757C2semidirect
6. C4×D1192C2semidirect
7. C8×D596C2semidirect
8. #493×C149C2semidirect
10. C2×D4×D149C22semidirect
12. C2×#14558721C22semidirect
14. C2×C8×D149C22semidirect
16. #18011882C22semidirect
19. C4×D596C22semidirect
20. #18011845C22semidirect
21. C4⋊#11924746C22semidirect
22. #18011833C22semidirect
23. #18011832C22semidirect
24. #18011823C22semidirect
25. C2×D8×C149C22semidirect
26. C2×D8×C149C22semidirect
27. #127×C149C22semidirect
28. C4×C8×C149C22semidirect
39. D1192D4semidirect
62. D596D8semidirect
63. D596C2×D4semidirect
81. C8×C149C2×D4semidirect
92. C2×D149C2×D8semidirect
94. C4×C149C2×D8semidirect
105. C149D4×D8semidirect
109. #493D149semidirect
120. C2×D8C2×D149semidirect
121. C2×D8C2×D149semidirect
123. #127C2×D149semidirect
134. C4×C8C2×D149semidirect
187. C8D4×D149semidirect
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
#237502602
#237498582
#237498172
#237497572
C4×D11922
C8×D5962
#493×C1492
D4×D8149