Finite Group Databasebeta

← #34043383

Subgroups — #34043383

Order 19072.

252 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 67 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#23750173C211yesmaximal, characteristic
2#23749681C211yesmaximal, characteristic, complemented
3C4⋊C8×D149C211yesmaximal, characteristic, complemented
4#23749373C211yesmaximal, characteristic, complemented
5#23749373C211yesmaximal, characteristic, complemented
6#23749369C211yesmaximal, characteristic, complemented
7#331×C149C211yesmaximal, characteristic, complemented
8C2×#14558735C412yes—
9C2×C8×D149—21no—
10#18011911C2211yescharacteristic
11#18011898C412yes—
12#18011882—21no—
13#18011882—21no—
14D4×Dic149—21no—
15D4×Dic149—21no—
16C42×D149C2211yescharacteristic
17C4⋊#11924746C2211yescharacteristic
18C4⋊#11924746C2211yescharacteristic
19#18011840—21no—
20#18011823—21no—
21#18011821—21no—
22#127×C149C2211yescharacteristic
23C4⋊C8×C149C2211yescharacteristic
24C4⋊C8×C149C2211yescharacteristic
25#14558735—44no—
26C2×Dic298C2×C412yes—
27C2×C22⋊D149—22no—
28C22×Dic149—22no—
29C2×C4×D149C2×C411yescharacteristic
30C2×C4×D149D411yescharacteristic
31C2×C4×D149D411yescharacteristic
32C2×#11924746—21no—
33C2×#11924746—21no—
34C8×D149—42no—
35C4⋊Dic149—21no—
36C4⋊Dic149—21no—
37C22⋊Dic149—22no—
38C22⋊Dic149—22no—
39C4×Dic149C2×C411yescharacteristic
40C4×Dic149D411yescharacteristic
41C4×Dic149D411yescharacteristic
42C2×D4×C149—21no—
43C2×D4×C149—21no—
44C2×D4×C149C2×C412yes—
45C2×C8×C149—21no—
46C2×C8×C149—21no—
47C42×C149C2311yescharacteristic
48C22×D149C22⋊C411yescharacteristic
49Dic298—42no—
50C22⋊D149—44no—
51C2×Dic149—22no—
52C2×Dic149—44no—
53C2×Dic149C22⋊C411yescharacteristic
54C2×Dic149C22⋊C411yescharacteristic
55C2×Dic149C22⋊C411yescharacteristic
56C4×D149—22no—
57C4×D149—21no—
58C4×D149—21no—
59C4×D149—21no—
60C4×D149—21no—
61#11924746—41no—
62#11924746—41no—
63C23×C149—22no—
64D4×C149—42no—
65D4×C149—41no—
66D4×C149—41no—
67D4×C149—41no—
68D4×C149—41no—
69C2×C4×C149C22×C411yescharacteristic
70C2×C4×C149C2×D411yescharacteristic
71C2×C4×C149C2×D411yescharacteristic
72C8×C149—41no—
73C8×C149—41no—
74C22×C149—42no—
75C22×C149—42no—
76C22×C149—42no—
77C22×C149C2×C22⋊C411yescharacteristic
78C2×D149—21no—
79C2×D149—21no—
80C2×D149#10012yes—
81C4×C149—21no—
82C4×C149#13511yescharacteristic
83C4×C149#13511yescharacteristic
84C4×C149AGL(1,ℤ/8)11yescharacteristic
85C4×C149#13711yescharacteristic
86Dic149—21no—
87Dic149—21no—
88Dic149—21no—
89Dic149—42no—
90C2×C149—82no—
91C2×C149C2×#10011yescharacteristic
92C2×C149#41611yescharacteristic
93C2×C149#41711yescharacteristic
94D149—22no—
95C149#155111yescharacteristic, complemented, Sylow
96#1551—1491nomaximal, Sylow
97#532—1491no—
98#432—1491no—
99C2×C4⋊C8—1491no—
100#333—1491no—
101#333—1491no—
102#331—1491no—
103#331D14911yescharacteristic, complemented
104C2×#41—1492no—
105C22×C8—2981no—
106C4⋊Q8—1491no—
107#127C2×D14911yescharacteristic
108#124—1492no—
109#121—2981no—
110#121—2981no—
111C4×D4—2981no—
112C4×D4—2981no—
113C2×C42—1491no—
114C4⋊C8—2981no—
115C4⋊C8—1491no—
116C4⋊C8—1491no—
117C4⋊C8C2×D14911yescharacteristic
118C4⋊C8C2×D14911yescharacteristic
119C22⋊C8—2981no—
120#97—2981no—
121#41—5964no—
122C2×Q8—1492no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—2982no—
126C2×D4C4×D14912yes—
127C22×C4—2982no—
128C22×C4—1491no—
129C22×C4—1491no—
130C22×C4—1491no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—2981no—
134C2×C8—2981no—
135C2×C8—5962no—
136C4⋊C4—2981no—
137C4⋊C4—2981no—
138C22⋊C4—2982no—
139C22⋊C4—2982no—
140C42—1491no—
141C42—1491no—
142C42—1491no—
143C42C22×D14911yescharacteristic
144C23—22no—
145C23—1491no—
146Q8—5962no—
147D4—42no—
148D4—41no—
149D4—41no—
150D4—41no—
151D4—41no—
152D4—5964no—
153C2×C4—2982no—
154C2×C4—2981no—
155C2×C4—2981no—
156C2×C4—2981no—
157C2×C4—2981no—
158C2×C4—2982no—
159C2×C4—5964no—
160C2×C4—1491no—
161C2×C4—1491no—
162C2×C4—1491no—
163C2×C4C2×C4×D14911yescharacteristic
164C2×C4D4×D14911yescharacteristic
165C2×C4D4×D14911yescharacteristic
166C8—41no—
167C8—41no—
168C8—5961no—
169C8—5961no—
170C22—42no—
171C22—42no—
172C22—42no—
173C22—2981no—
174C22—2981no—
175C22—1492no—
176C22C22⋊C4×D14911yescharacteristic
177C4—21no—
178C4—2981no—
179C4—2981no—
180C4—2981no—
181C4—5962no—
182C4#1801193011yescharacteristic
183C4#1801193211yescharacteristic
184C4#1801193511yescharacteristic
185C4#1801194011yescharacteristic
186C2—82no—
187C2—2982no—
188C2#100×D14911yescharacteristic
189C2#2374961811yescharacteristic
190C2#2374962311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D149
commutatorC2×C4×C149C22×C4
FrattiniC42C22×D149
Fitting#331×C149C2
socleC22×C149C2×C22⋊C4
prime radical#23750173C2
cosocleC42×C149C23
hypercenter#331D149
hypocenterC149#1551
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #23749681C2semidirect
3. C4⋊C8×D149C2semidirect
4. #23749373C2semidirect
5. #23749373C2semidirect
6. #23749369C2semidirect
7. #331×C149C2semidirect
95. C149#1551semidirect
103. #331D149semidirect

Maximal subgroups

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

subgroupindex
#237501732
#237496812
C4⋊C8×D1492
#237493732
#237493692
#331×C1492
#1551149