Finite Group Databasebeta

← #34055556

Subgroups — #34055556

Order 19072.

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

normal subgroups only

This group has 442 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
1#23750189C212yesmaximal, complemented
2#23749950C214yesmaximal, complemented
3#23749878C212yesmaximal, complemented
4#23749861C212yesmaximal, complemented
5#23749761C214yesmaximal, complemented
6#408×C149C211yesmaximal, characteristic, complemented
7C22×D596C2212yescomplemented
8C2×D1192C2212yes—
9C2×D1192C2212yes—
10#18011907—22no—
11#18011900—22no—
12#18011885C2214yes—
13#18011885C2214yescomplemented
14#18011879—22no—
15#18011879—22no—
16#18011870C2212yescomplemented
17#18011845C2212yescomplemented
18#18011843C2212yescomplemented
19#18011833C2214yescomplemented
20#18011833C2214yescomplemented
21C2×#41×C149C2211yescharacteristic
22C2×M16×C149C2211yescharacteristic, complemented
23C22×C8×C149C2211yescharacteristic, complemented
24C22⋊C8×C149C2214yescomplemented
25C23×D149—22no—
26C2×D596—22no—
27C2×D596—42no—
28C2×D596—42no—
29C2×D596C2314yes—
30C2×C22⋊D149—24no—
31C2×C22⋊D149—24no—
32D1192—42no—
33D1192—42no—
34C4⋊Dic149C2314yes—
35C22⋊Dic149—22no—
36#14558713—24no—
37#14558713—24no—
38C4×Dic149—22no—
39#41×C149—41no—
40#41×C149—41no—
41C2×Q8×C149D411yescharacteristic
42C2×D4×C149D412yes—
43C2×D4×C149D411yescharacteristic
44C22×C4×C149C2312yes—
45C22×C4×C149C2311yescharacteristic
46M16×C149—41no—
47C2×C8×C149—41no—
48C2×C8×C149C2312yes—
49C2×C8×C149C2312yes—
50C22×D149—24no—
51C22×D149—44no—
52C22×D149—84no—
53D596—24no—
54D596—24no—
55D596—44no—
56C22⋊D149—84no—
57C22⋊D149—84no—
58C2×Dic149—24no—
59C23×C149C2×D411yescharacteristic
60C23×C149C2×D412yes—
61Q8×C149—41no—
62D4×C149—41no—
63D4×C149—42no—
64C2×C4×C149—22no—
65C2×C4×C149—22no—
66C2×C4×C149—21no—
67C2×C4×C149—21no—
68C2×C4×C149C2×D412yes—
69C2×C4×C149C2×D411yescharacteristic
70C2×C4×C149C2411yescharacteristic
71C8×C149—22no—
72C8×C149—22no—
73C22×C149—21no—
74C22×C149—22no—
75C22×C149—22no—
76C22×C149—24no—
77C22×C149C22×D411yescharacteristic
78C2×D149—44no—
79C2×D149—44no—
80C2×D149—44no—
81C2×D149—88no—
82C4×C149—21no—
83C4×C149—22no—
84C4×C149H(5,𝔽2)11yescharacteristic
85C4×C149H(5,𝔽2)11yescharacteristic
86Dic149—44no—
87C2×C149—42no—
88C2×C149—41no—
89C2×C149#53411yescharacteristic
90C2×C149#57612yes—
91D149—84no—
92C149#319911yescharacteristic, complemented, Sylow
93#3199—1491nomaximal, Sylow
94#535—1492no—
95#482—1494no—
96#469—1492no—
97#466—1492no—
98#447—1494no—
99#408D14911yescharacteristic, complemented
100C2×#41C2×D14911yescharacteristic
101C22×D4—1492no—
102C2×D8—1492no—
103C2×D8—1492no—
104C2×M16C2×D14911yescharacteristic, complemented
105C22×C8C2×D14911yescharacteristic, complemented
106#127—2982no—
107#124—2982no—
108#121—1494no—
109#121—1494no—
110#120—2982no—
111#120—2982no—
112#117—1492no—
113#107—1492no—
114#106—1492no—
115#102—1494no—
116#102—1494no—
117C22⋊C8C2×D14914yescomplemented
118C24—2982no—
119#41—41no—
120#41—41no—
121C2×Q8D59611yescharacteristic
122C2×D4—2984no—
123C2×D4—2984no—
124C2×D4—2982no—
125C2×D4—5962no—
126C2×D4—5962no—
127C2×D4—1494no—
128C2×D4D59611yescharacteristic
129C2×D4D59612yes—
130C22×C4C22×D14912yes—
131C22×C4C22×D14911yescharacteristic
132D8—5962no—
133D8—5962no—
134M16—41no—
135C2×C8—41no—
136C2×C8C22×D14912yes—
137C2×C8C22×D14912yes—
138C4⋊C4—1494no—
139C22⋊C4—2982no—
140C22⋊C4—2984no—
141C22⋊C4—2984no—
142C42—2982no—
143C23—2984no—
144C23—5964no—
145C23—11924no—
146C23C2×D59612yes—
147C23C2×D59611yescharacteristic
148Q8—41no—
149D4—42no—
150D4—41no—
151D4—2984no—
152D4—2984no—
153D4—5964no—
154D4—11924no—
155D4—11924no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—2984no—
161C2×C4C2×D59612yes—
162C2×C4C2×D59611yescharacteristic
163C2×C4C23×D14911yescharacteristic
164C8—22no—
165C8—22no—
166C22—22no—
167C22—24no—
168C22—22no—
169C22—21no—
170C22—5964no—
171C22—5964no—
172C22—5964no—
173C22—11928no—
174C22C22×D59611yescharacteristic
175C4—22no—
176C4—21no—
177C4—5964no—
178C4#1801195611yescharacteristic
179C4#1801195611yescharacteristic
180C2—42no—
181C2—41no—
182C2—11924no—
183C2#2375018711yescharacteristic
184C2#2375043012yes—
subgroupG/H
centerC22C22×D596
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#408×C149C2
socleC22×C149C22×D4
hypercenter#408D149
hypocenterC149#3199
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
1. #23750189C2semidirect
2. #23749950C2semidirect
3. #23749878C2semidirect
4. #23749861C2semidirect
5. #23749761C2semidirect
6. #408×C149C2semidirect
7. C22×D596C22semidirect
13. #18011885C22semidirect
16. #18011870C22semidirect
17. #18011845C22semidirect
18. #18011843C22semidirect
19. #18011833C22semidirect
20. #18011833C22semidirect
22. C2×M16×C149C22semidirect
23. C22×C8×C149C22semidirect
24. C22⋊C8×C149C22semidirect
92. C149#3199semidirect
99. #408D149semidirect
104. C2×M16C2×D149semidirect
105. C22×C8C2×D149semidirect
117. C22⋊C8C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237501892
#237499502
#237498782
#237498612
#237497612
#408×C1492
#3199149