Finite Group Databasebeta

← #34060966

Subgroups — #34060966

Order 19072.

286 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 54 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×#18011970C212yesmaximal, complemented
2#23750531C212yesmaximal, complemented
3#23750529C212yesmaximal, complemented
4#23750189C211yesmaximal, characteristic
5C2×C22⋊#10597010—22no—
6#18011970—22no—
7#18011970C2214yes—
8C22×D596C2211yescharacteristic
9#18011907C411yescharacteristic, complemented
10#18011907C2211yescharacteristic
11#18011900C411yescharacteristic, complemented
12#18011900C2211yescharacteristic
13#18011885—22no—
14#18011879—22no—
15#18011870C411yescharacteristic, complemented
16C2×#41×C149C411yescharacteristic, complemented
17C22×#10597010—42no—
18C22⋊#10597010—24no—
19C22⋊#10597010—42no—
20C23×D149D412yes—
21C2×D596—42no—
22C2×D596C2×C411yescharacteristic
23C2×D596D412yes—
24C2×D596C2311yescharacteristic
25C2×C22⋊D149—22no—
26C2×C22⋊D149—22no—
27C4⋊Dic149—21no—
28C22⋊Dic149—21no—
29#14558713—22no—
30#14558713—22no—
31C4×Dic149C2×C411yescharacteristic, complemented
32C4×Dic149C2×C411yescharacteristic, complemented
33#41×C149—42no—
34C2×Q8×C149C2×C411yescharacteristic, complemented
35C2×D4×C149—21no—
36C2×D4×C149C2×C411yescharacteristic, complemented
37C22×C4×C149—21no—
38C22×C4×C149C2×C411yescharacteristic
39C2×#10597010—44no—
40C2×#10597010—84no—
41C22×D149—22no—
42C22×D149—22no—
43C22×D149—82no—
44C22×D149C22⋊C412yes—
45C22×D149C2×D412yes—
46D596—41no—
47D596—42no—
48D596—41no—
49C22⋊D149—82no—
50C22⋊D149—82no—
51C2×Dic149—21no—
52C2×Dic149—21no—
53C23×C149—21no—
54C23×C149C22⋊C411yescharacteristic
55Q8×C149—41no—
56D4×C149—41no—
57D4×C149—42no—
58C2×C4×C149—22no—
59C2×C4×C149—21no—
60C2×C4×C149—42no—
61C2×C4×C149C22⋊C411yescharacteristic
62C2×C4×C149C22×C411yescharacteristic
63C22×C149—41no—
64C22×C149—42no—
65C22×C149—41no—
66C22×C149#9912yes—
67C22×C149C2×C22⋊C411yescharacteristic
68C2×D149—22no—
69C2×D149—22no—
70C2×D149—44no—
71C2×D149—42no—
72C2×D149—42no—
73C2×D149—82no—
74#10597010—84no—
75C4×C149—21no—
76C4×C149—21no—
77C4×C149—41no—
78Dic149—41no—
79Dic149—41no—
80C2×C149—21no—
81C2×C149—22no—
82C2×C149—81no—
83C2×C149C2×#9911yescharacteristic
84D149—42no—
85D149—42no—
86C149#212711yescharacteristic, complemented, Sylow
87#2127—1491nomaximal, Sylow
88#535—1491no—
89C2×#99—1492no—
90#354—1492no—
91#353—1492no—
92C2×#41#1059701011yescharacteristic, complemented
93C22×D4—1491no—
94#127—1491no—
95#127—1491no—
96#124—1491no—
97#124—1491no—
98#121—2982no—
99#120—2982no—
100#117—1491no—
101C2×C22⋊C4—2982no—
102#99—2982no—
103#99—1494no—
104C24—1492no—
105#41—42no—
106C2×Q8C2×#1059701011yescharacteristic, complemented
107C2×D4—21no—
108C2×D4—2982no—
109C2×D4—2982no—
110C2×D4—5962no—
111C2×D4—1492no—
112C2×D4—1491no—
113C2×D4—1491no—
114C2×D4C2×#1059701011yescharacteristic, complemented
115C22×C4—21no—
116C22×C4—5962no—
117C22×C4C2×#1059701011yescharacteristic
118C4⋊C4—2981no—
119C22⋊C4—2982no—
120C22⋊C4—2982no—
121C22⋊C4—2981no—
122C22⋊C4—2984no—
123C22⋊C4—5962no—
124C42—1491no—
125C42—1491no—
126C23—21no—
127C23—2982no—
128C23—2982no—
129C23—1492no—
130C23—1492no—
131C23—11922no—
132C23C22⋊#1059701011yescharacteristic
133Q8—41no—
134D4—41no—
135D4—42no—
136D4—5962no—
137D4—5961no—
138D4—5961no—
139D4—11922no—
140D4—11922no—
141C2×C4—22no—
142C2×C4—21no—
143C2×C4—42no—
144C2×C4—2981no—
145C2×C4—2981no—
146C2×C4—5964no—
147C2×C4—11924no—
148C2×C4C22⋊#1059701011yescharacteristic
149C2×C4C22×#1059701011yescharacteristic
150C22—41no—
151C22—42no—
152C22—41no—
153C22—2982no—
154C22—2982no—
155C22—5962no—
156C22—5962no—
157C22—5964no—
158C22—11922no—
159C22#1801196912yes—
160C22C2×C22⋊#1059701011yescharacteristic
161C4—21no—
162C4—21no—
163C4—41no—
164C4—5961no—
165C4—5961no—
166C4—11924no—
167C2—21no—
168C2—22no—
169C2—81no—
170C2—5962no—
171C2—5962no—
172C2C2×#1801196911yescharacteristic
subgroupG/H
centerC2C2×#18011969
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC2×#41×C149C4
socleC2×C149C2×#99
prime radical#23750189C2
cosocleC2×D596C23
hypercenterC2×#41#10597010
hypocenterC149#2127
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C23 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#18011970C2semidirect
2. #23750531C2semidirect
3. #23750529C2semidirect
9. #18011907C4semidirect
11. #18011900C4semidirect
15. #18011870C4semidirect
16. C2×#41×C149C4semidirect
31. C4×Dic149C2×C4semidirect
32. C4×Dic149C2×C4semidirect
34. C2×Q8×C149C2×C4semidirect
36. C2×D4×C149C2×C4semidirect
86. C149#2127semidirect
92. C2×#41#10597010semidirect
106. C2×Q8C2×#10597010semidirect
114. C2×D4C2×#10597010semidirect

Maximal subgroups

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

subgroupindex
C2×#180119702
#237505312
#237505292
#237501892
#2127149