Finite Group Databasebeta

← #34060002

Subgroups — #34060002

Order 19072.

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

normal subgroups only

This group has 212 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#23750642C211yesmaximal, characteristic, complemented
2#23750641C211yesmaximal, characteristic, complemented
3#23750475C212yesmaximal, complemented
4D4⋊#11924753C212yesmaximal, complemented
5#23750156C211yesmaximal, characteristic
6#18011978—21no—
7C4⋊#11924753C2212yes—
8C22⋊#11924753—21no—
9C22⋊#11924753—21no—
10C4×#11924753—21no—
11C4×#11924753C2212yes—
12#18011904—21no—
13#18011902C411yescharacteristic
14#18011898C411yescharacteristic
15#18011892—21no—
16#18011890C411yescharacteristic
17#18011876C2211yescharacteristic
18D4×Dic149—21no—
19D4×Dic149C2211yescharacteristic
20#18011867—21no—
21C2×C4×Dic149C2211yescharacteristic
22#121×C149C411yescharacteristic
23C2×#11924753—22no—
24C2×#11924753—22no—
25C2×Dic298C2×C411yescharacteristic
26C22×Dic149—21no—
27C22×Dic149D411yescharacteristic
28C22×Dic149D411yescharacteristic
29C4⋊Dic149—21no—
30C4⋊Dic149C2×C411yescharacteristic
31#14558715—21no—
32#14558715—21no—
33#14558715—21no—
34C22⋊Dic149—21no—
35C22⋊Dic149—21no—
36C22⋊Dic149—21no—
37C22⋊Dic149—21no—
38C4×Dic149—21no—
39C4×Dic149C2×C411yescharacteristic
40C4×Dic149D411yescharacteristic
41C4×Dic149D411yescharacteristic
42C4×Dic149C2311yescharacteristic
43C2×D4×C149—21no—
44C2×D4×C149C2×C411yescharacteristic
45C22×C4×C149C2×C411yescharacteristic
46C4⋊C4×C149C2×C411yescharacteristic
47C22⋊C4×C149—21no—
48#11924753—42no—
49#11924753—42no—
50Dic298—22no—
51C2×Dic149—22no—
52C2×Dic149—21no—
53C2×Dic149—21no—
54C2×Dic149—41no—
55C2×Dic149—42no—
56C2×Dic149C22⋊C411yescharacteristic
57C2×Dic149C22⋊C411yescharacteristic
58C2×Dic149C2×D411yescharacteristic
59C2×Dic149C2×D411yescharacteristic
60C23×C149—21no—
61C23×C149C22⋊C411yescharacteristic
62D4×C149—22no—
63D4×C149—42no—
64C2×C4×C149—22no—
65C2×C4×C149—21no—
66C2×C4×C149C22⋊C411yescharacteristic
67C2×C4×C149C22×C411yescharacteristic
68C22×C149—21no—
69C22×C149—21no—
70C22×C149—21no—
71C22×C149—41no—
72C22×C149—41no—
73C22×C149—41no—
74C22×C149C2×C22⋊C411yescharacteristic
75C4×C149—21no—
76C4×C149—41no—
77C4×C149#13112yes—
78Dic149—21no—
79Dic149—21no—
80Dic149—21no—
81Dic149—41no—
82Dic149—41no—
83Dic149#13512yes—
84C2×C149—41no—
85C2×C149—81no—
86C2×C149#40811yescharacteristic
87C2×C149#41611yescharacteristic
88C2×C149#42111yescharacteristic
89C149#148211yescharacteristic, complemented, Sylow
90#1482—1491nomaximal, Sylow
91#529—1491no—
92#431—1491no—
93#431—1491no—
94Q8⋊C8—1492no—
95D4⋊C8—1492no—
96#126—2981no—
97#125—1491no—
98#124—1491no—
99#123—2981no—
100C22⋊Q8—1491no—
101#121#1059701011yescharacteristic
102C4×Q8—1491no—
103C4×D4—2981no—
104C4×D4—1491no—
105#117—2981no—
106C2×C42—1491no—
107C4⋊C8—2981no—
108C4⋊C8—1492no—
109C22⋊C8—2981no—
110C22⋊C8—2981no—
111C4×C8—2981no—
112C4×C8—1492no—
113C2×Q8—1491no—
114C2×D4—21no—
115C2×D4C2×#1059701011yescharacteristic
116C22×C4—2981no—
117C22×C4—1491no—
118C22×C4—1491no—
119C22×C4C2×#1059701011yescharacteristic
120C2×C8—2982no—
121C2×C8—2982no—
122C4⋊C4—2981no—
123C4⋊C4—2981no—
124C4⋊C4—2981no—
125C4⋊C4—2981no—
126C4⋊C4—1491no—
127C4⋊C4C2×#1059701011yescharacteristic
128C22⋊C4—21no—
129C22⋊C4—2981no—
130C22⋊C4—2981no—
131C22⋊C4—2981no—
132C22⋊C4—2981no—
133C42—2981no—
134C42—1491no—
135C42—1491no—
136C42—1491no—
137C42—1491no—
138C23—21no—
139C23C22⋊#1059701011yescharacteristic
140Q8—2982no—
141D4—22no—
142D4—42no—
143C2×C4—22no—
144C2×C4—21no—
145C2×C4—2982no—
146C2×C4—2981no—
147C2×C4—2981no—
148C2×C4—5961no—
149C2×C4—5962no—
150C2×C4—1491no—
151C2×C4—1491no—
152C2×C4—1491no—
153C2×C4—1491no—
154C2×C4C22⋊#1059701011yescharacteristic
155C2×C4C22×#1059701011yescharacteristic
156C8—5962no—
157C8—5962no—
158C22—21no—
159C22—21no—
160C22—21no—
161C22—41no—
162C22—41no—
163C22—41no—
164C22C2×C22⋊#1059701011yescharacteristic
165C4—21no—
166C4—41no—
167C4—2981no—
168C4—2981no—
169C4—2981no—
170C4—5961no—
171C4—5961no—
172C4—1492no—
173C4#1801199812yes—
174C2—41no—
175C2—81no—
176C2#2375059811yescharacteristic
177C2#2375061511yescharacteristic
178C2#2375062311yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
Fitting, prime radical#121×C149C4
socleC22×C149C2×C22⋊C4
cosocleC4×Dic149C23
hypercenter#121#10597010
hypocenterC149#1482
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #23750642C2semidirect
2. #23750641C2semidirect
3. #23750475C2semidirect
4. D4⋊#11924753C2semidirect
89. C149#1482semidirect

Maximal subgroups

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

subgroupindex
#237506422
#237506412
#237504752
D4⋊#119247532
#237501562
#1482149