Finite Group Databasebeta

← #34059998

Subgroups — #34059998

Order 19072.

260 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 70 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
2D149⋊(C4⋊C8)C211yesmaximal, characteristic, complemented
3#23750473C214yesmaximal, complemented
4#23750176C211yesmaximal, characteristic
5C2×D149⋊C8—21no—
6#18011978—21no—
7C4⋊#11924753—21no—
8C4⋊#11924753C2212yes—
9#18011968—21no—
10C4×#11924753C2212yes—
11C2×#14558737—21no—
12#18011908C411yescharacteristic
13#18011900—21no—
14#18011886—21no—
15#18011886C412yes—
16#18011873—21no—
17#18011873C2212yes—
18C42×D149C2211yescharacteristic
19C4⋊Q8×C149C411yescharacteristic
20D149⋊C8—42no—
21C2×#11924753—22no—
22C2×#11924753—22no—
23#14558737—42no—
24#14558737—42no—
25C2×D596—22no—
26C2×D596—21no—
27C2×D596—21no—
28C2×D596C2×C412yes—
29C2×C4×D149—22no—
30C2×C4×D149C2×C411yescharacteristic
31C2×C4×D149D411yescharacteristic
32C2×C4×D149D411yescharacteristic
33#14558713—22no—
34#14558713—22no—
35C4×Dic149D411yescharacteristic
36C4×Dic149D411yescharacteristic
37C4×Dic149C2311yescharacteristic
38C2×Q8×C149—21no—
39C4⋊C4×C149—21no—
40C4⋊C4×C149C2×C412yes—
41C42×C149C2×C411yescharacteristic
42#11924753—42no—
43#11924753—42no—
44C22×D149—22no—
45C22×D149C22⋊C411yescharacteristic
46D596—24no—
47D596—42no—
48D596—44no—
49D596—42no—
50C2×Dic149C22⋊C411yescharacteristic
51C2×Dic149C2×D411yescharacteristic
52C2×Dic149C2×D411yescharacteristic
53C4×D149—22no—
54C4×D149—41no—
55C4×D149—42no—
56C4×D149—42no—
57C4×D149D812yes—
58C4×D149SD1612yes—
59Q8×C149—42no—
60C2×C4×C149—22no—
61C2×C4×C149C22⋊C411yescharacteristic
62C2×C4×C149C22⋊C411yescharacteristic
63C2×C4×C149C22×C411yescharacteristic
64C22×C149C2×C22⋊C411yescharacteristic
65C2×D149—21no—
66C2×D149—21no—
67C2×D149—42no—
68C2×D149—42no—
69C2×D149—42no—
70C2×D149#10212yes—
71C4×C149—21no—
72C4×C149—42no—
73C4×C149#10212yes—
74C4×C149#13112yes—
75Dic149—21no—
76Dic149—21no—
77Dic149C2×D811yescharacteristic
78Dic149C2×SD1611yescharacteristic
79C2×C149#40811yescharacteristic
80C2×C149C2×#10211yescharacteristic
81C2×C149#42111yescharacteristic
82D149—22no—
83D149—82no—
84C149#148011yescharacteristic, complemented, Sylow
85#1480—1491nomaximal, Sylow
86#532—1491no—
87#431—1491no—
88C2×C4⋊C8—1491no—
89D4⋊C8—1494no—
90C2×#41—2981no—
91C22×C8—2981no—
92C4⋊Q8#1059701011yescharacteristic
93#127—1491no—
94#124—2981no—
95#121—2981no—
96#121—1492no—
97C4×D4—2981no—
98C4×D4—1492no—
99C2×C42—1491no—
100C4⋊C8—2981no—
101C4⋊C8—2981no—
102C4⋊C8—1492no—
103C22⋊C8—2981no—
104C4×C8—1492no—
105#41—5962no—
106#41—5962no—
107C2×Q8—21no—
108C2×D4—2982no—
109C2×D4—2981no—
110C2×D4—2981no—
111C2×D4—1492no—
112C22×C4—2982no—
113C22×C4—1491no—
114C22×C4—1491no—
115C22×C4—1491no—
116C2×C8—2982no—
117C2×C8—2982no—
118C2×C8—5962no—
119C4⋊C4—21no—
120C4⋊C4C2×#1059701012yes—
121C22⋊C4—2982no—
122C22⋊C4—2982no—
123C42—1491no—
124C42—1491no—
125C42—1491no—
126C42C2×#1059701011yescharacteristic
127C23—2982no—
128C23—1491no—
129Q8—42no—
130D4—2984no—
131D4—5962no—
132D4—5964no—
133D4—5962no—
134C2×C4—22no—
135C2×C4—2982no—
136C2×C4—5961no—
137C2×C4—5962no—
138C2×C4—5962no—
139C2×C4—1491no—
140C2×C4—1491no—
141C2×C4—1491no—
142C2×C4—1492no—
143C2×C4—1492no—
144C2×C4C22⋊#1059701011yescharacteristic
145C2×C4C22⋊#1059701011yescharacteristic
146C2×C4C22×#1059701011yescharacteristic
147C8—5962no—
148C8—5962no—
149C22—2981no—
150C22—2981no—
151C22—5962no—
152C22—5962no—
153C22—5962no—
154C22—1492no—
155C22C2×C22⋊#1059701011yescharacteristic
156C4—21no—
157C4—42no—
158C4—2981no—
159C4—2981no—
160C4—1491no—
161C4—1491no—
162C4#1801197312yes—
163C4#1801199912yes—
164C2—2982no—
165C2—11922no—
166C2#2375060011yescharacteristic
167C2C2×#1801197311yescharacteristic
168C2#2375062411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC4⋊Q8×C149C4
socleC22×C149C2×C22⋊C4
prime radical#23750176C2
cosocleC4×Dic149C23
hypercenterC4⋊Q8#10597010
hypocenterC149#1480
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #23750644C2semidirect
2. D149⋊(C4⋊C8)C2semidirect
3. #23750473C2semidirect
84. C149#1480semidirect

Maximal subgroups

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

subgroupindex
#237506442
D149⋊(C4⋊C8)2
#237504732
#237501762
#1480149