Finite Group Databasebeta

← #34060062

Subgroups — #34060062

Order 19072.

238 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 60 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#23750644C211yesmaximal, characteristic, complemented
2#23750561C211yesmaximal, characteristic, complemented
3#23750478C212yesmaximal, complemented
4#23750476C212yesmaximal
5#23750157C211yesmaximal, characteristic
6C2×C4×#10597010—21no—
7C4⋊#11924753—21no—
8#18011968C2212yes—
9C4×#11924753—21no—
10(C2×#10597010)⋊C4—21no—
11(C2×#10597010)⋊C4C2212yes—
12#18011904—21no—
13#18011902C411yescharacteristic, complemented
14#18011898C411yescharacteristic, complemented
15#18011893—21no—
16#18011891C2211yescharacteristic
17#18011882C2211yescharacteristic
18C4×Dic298C411yescharacteristic, complemented
19C4×C22⋊D149—21no—
20#18011870—21no—
21C42×D149C2211yescharacteristic
22C4×D4×C149C411yescharacteristic, complemented
23C22×#10597010—22no—
24C2×#11924753—22no—
25C4×#10597010—24no—
26C2×Dic298C2×C411yescharacteristic
27C2×C22⋊D149—21no—
28C2×C4×D149D411yescharacteristic
29C2×C4×D149D411yescharacteristic
30C2×C4×D149C2311yescharacteristic
31C4⋊Dic149—21no—
32C4⋊Dic149—21no—
33C4⋊Dic149C2×C411yescharacteristic
34#14558715—21no—
35#14558715—21no—
36C22⋊Dic149—21no—
37C22⋊Dic149—21no—
38C22⋊Dic149—21no—
39#14558713—21no—
40C4×Dic149—21no—
41C4×Dic149C2×C411yescharacteristic
42C4×Dic149D411yescharacteristic
43C4×Dic149D411yescharacteristic
44C2×D4×C149C2×C411yescharacteristic
45C22×C4×C149—21no—
46C4⋊C4×C149C2×C411yescharacteristic
47C22⋊C4×C149—21no—
48C42×C149C2×C411yescharacteristic
49C2×#10597010—24no—
50C2×#10597010—42no—
51C2×#10597010—42no—
52#11924753—42no—
53C22×D149C2×D411yescharacteristic
54Dic298—41no—
55C22⋊D149—42no—
56C2×Dic149—21no—
57C2×Dic149—21no—
58C2×Dic149C22⋊C411yescharacteristic
59C2×Dic149C22⋊C411yescharacteristic
60C2×Dic149C2×D411yescharacteristic
61C4×D149—22no—
62C4×D149—22no—
63C4×D149—41no—
64C23×C149—21no—
65D4×C149—41no—
66C2×C4×C149—21no—
67C2×C4×C149—42no—
68C2×C4×C149C22⋊C411yescharacteristic
69C2×C4×C149C22⋊C411yescharacteristic
70C2×C4×C149C22×C411yescharacteristic
71C22×C149—41no—
72C22×C149—41no—
73C22×C149—41no—
74C22×C149C2×C22⋊C411yescharacteristic
75C2×D149—21no—
76C2×D149—21no—
77C2×D149#13512yes—
78#10597010—44no—
79C4×C149—21no—
80C4×C149—21no—
81C4×C149—41no—
82C4×C149#10412yes—
83Dic149—21no—
84Dic149—21no—
85Dic149—21no—
86Dic149—41no—
87Dic149—41no—
88C2×C149—81no—
89C2×C149#41011yescharacteristic
90C2×C149#41611yescharacteristic
91C2×C149C2×#10411yescharacteristic
92D149—22no—
93C149#150011yescharacteristic, complemented, Sylow
94#1500—1491nomaximal, Sylow
95#529—1491no—
96#431—1491no—
97#376—1491no—
98#328—1492no—
99#327—1492no—
100#126—2981no—
101#125—1491no—
102#124—1491no—
103#123—2981no—
104C22⋊Q8—1491no—
105#121—1491no—
106C4×Q8—1491no—
107C4×D4—2981no—
108C4×D4#1059701011yescharacteristic, complemented
109#117—2981no—
110C2×C42—2981no—
111C2×C42—1491no—
112C4⋊C8—2981no—
113C22⋊C8—1492no—
114C4×C8—2981no—
115#95—2981no—
116#95—1492no—
117C2×Q8—1491no—
118C2×D4—2981no—
119C2×D4C2×#1059701011yescharacteristic
120C22×C4—21no—
121C22×C4—2982no—
122C22×C4—1491no—
123C22×C4—1491no—
124C22×C4—1491no—
125C2×C8—2982no—
126C4⋊C4—2981no—
127C4⋊C4—2981no—
128C4⋊C4—2981no—
129C4⋊C4—2981no—
130C4⋊C4—1491no—
131C4⋊C4C2×#1059701011yescharacteristic
132C22⋊C4—21no—
133C22⋊C4—2981no—
134C22⋊C4—2981no—
135C22⋊C4—2981no—
136C22⋊C4—2981no—
137C42—2984no—
138C42—2981no—
139C42—1491no—
140C42—1491no—
141C42—1491no—
142C42C2×#1059701011yescharacteristic
143C23—21no—
144C23—1491no—
145Q8—5961no—
146D4—41no—
147D4—5962no—
148C2×C4—21no—
149C2×C4—42no—
150C2×C4—2982no—
151C2×C4—2982no—
152C2×C4—2984no—
153C2×C4—2981no—
154C2×C4—2981no—
155C2×C4—5961no—
156C2×C4—5962no—
157C2×C4—5962no—
158C2×C4—1491no—
159C2×C4—1491no—
160C2×C4—1491no—
161C2×C4C22⋊#1059701011yescharacteristic
162C2×C4C22⋊#1059701011yescharacteristic
163C2×C4C22×#1059701011yescharacteristic
164C8—5962no—
165C22—41no—
166C22—41no—
167C22—41no—
168C22—2981no—
169C22—2981no—
170C22—1492no—
171C22C2×C22⋊#1059701011yescharacteristic
172C4—21no—
173C4—21no—
174C4—41no—
175C4—2981no—
176C4—2981no—
177C4—2981no—
178C4—5964no—
179C4—5961no—
180C4—5961no—
181C4#1801197512yes—
182C2—81no—
183C2—2982no—
184C2#2375060411yescharacteristic
185C2#2375061511yescharacteristic
186C2C2×#1801197511yescharacteristic
subgroupG/H
centerC2×C4C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC4×D4×C149C4
socleC22×C149C2×C22⋊C4
prime radical#18011882C22
cosocleC2×C4×D149C23
hypercenterC4×D4#10597010
hypocenterC149#1500
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #23750644C2semidirect
2. #23750561C2semidirect
3. #23750478C2semidirect
13. #18011902C4semidirect
14. #18011898C4semidirect
18. C4×Dic298C4semidirect
22. C4×D4×C149C4semidirect
93. C149#1500semidirect
108. C4×D4#10597010semidirect

Maximal subgroups

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

subgroupindex
#237506442
#237505612
#237504782
#237504762
#237501572
#1500149