Finite Group Databasebeta

← #34043365

Subgroups — #34043365

Order 19072.

260 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 73 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#23749647C211yesmaximal, characteristic, complemented
3C4⋊C8×D149C211yesmaximal, characteristic, complemented
4#23749372C211yesmaximal, characteristic, complemented
5#23749370C211yesmaximal, characteristic, complemented
6#23749369C211yesmaximal, characteristic, complemented
7#331×C149C211yesmaximal, characteristic, complemented
8C2×#14558735—21no—
9C2×#14558719—21no—
10C2×C8×D149—21no—
11#18011911C2211yescharacteristic
12#18011898—21no—
13#18011882—21no—
14#18011882C412yes—
15D4×Dic149—21no—
16D4×Dic149C412yes—
17C42×D149C2211yescharacteristic
18C4⋊#11924746C2211yescharacteristic
19C4⋊#11924746C2211yescharacteristic
20#18011840—21no—
21#18011840—21no—
22#127×C149C2211yescharacteristic
23C4⋊C8×C149C2211yescharacteristic
24C4⋊C8×C149C2211yescharacteristic
25#14558735—42no—
26#14558735—42no—
27C2×Dic298—21no—
28C2×C22⋊D149—22no—
29C22×Dic149—22no—
30C2×C4×D149C2×C411yescharacteristic
31C2×C4×D149D411yescharacteristic
32C2×C4×D149D411yescharacteristic
33#14558719—42no—
34C2×#11924746—21no—
35C2×#11924746—21no—
36C8×D149—42no—
37C4⋊Dic149—21no—
38C4⋊Dic149C2×C412yes—
39C22⋊Dic149—22no—
40C22⋊Dic149—22no—
41C4×Dic149C2×C411yescharacteristic
42C4×Dic149D411yescharacteristic
43C4×Dic149D411yescharacteristic
44C2×D4×C149—21no—
45C2×D4×C149—21no—
46C2×D4×C149C2×C412yes—
47C2×C8×C149—21no—
48C2×C8×C149—21no—
49C42×C149C2311yescharacteristic
50C22×D149C22⋊C411yescharacteristic
51Dic298—41no—
52Dic298—41no—
53C22⋊D149—44no—
54C2×Dic149—22no—
55C2×Dic149—44no—
56C2×Dic149C22⋊C411yescharacteristic
57C2×Dic149C22⋊C411yescharacteristic
58C2×Dic149C22⋊C411yescharacteristic
59C4×D149—21no—
60C4×D149—21no—
61C4×D149—41no—
62C4×D149D812yes—
63C4×D149SD1612yes—
64#11924746—41no—
65#11924746—41no—
66C23×C149—22no—
67D4×C149—42no—
68D4×C149—41no—
69D4×C149—41no—
70D4×C149—41no—
71D4×C149—41no—
72C2×C4×C149C22×C411yescharacteristic
73C2×C4×C149C2×D411yescharacteristic
74C2×C4×C149C2×D411yescharacteristic
75C8×C149—41no—
76C8×C149—41no—
77C22×C149—42no—
78C22×C149—42no—
79C22×C149—42no—
80C22×C149C2×C22⋊C411yescharacteristic
81C2×D149—21no—
82C2×D149—21no—
83C2×D149#10212yes—
84C4×C149—21no—
85C4×C149C2×D811yescharacteristic
86C4×C149C2×SD1611yescharacteristic
87C4×C149AGL(1,ℤ/8)11yescharacteristic
88C4×C149#13711yescharacteristic
89Dic149—21no—
90Dic149—21no—
91Dic149—42no—
92Dic149#10212yes—
93C2×C149—82no—
94C2×C149#41311yescharacteristic
95C2×C149C2×#10211yescharacteristic
96C2×C149#41711yescharacteristic
97D149—22no—
98C149#154711yescharacteristic, complemented, Sylow
99#1547—1491nomaximal, Sylow
100#532—1491no—
101#423—1491no—
102C2×C4⋊C8—1491no—
103#332—1491no—
104#332—1491no—
105#331—1491no—
106#331D14911yescharacteristic, complemented
107C2×#41—2981no—
108C2×M16—2981no—
109C22×C8—2981no—
110C4⋊Q8—1491no—
111#127C2×D14911yescharacteristic
112#124—2981no—
113#121—2981no—
114#121—1492no—
115C4×D4—2981no—
116C4×D4—1492no—
117C2×C42—1491no—
118C4⋊C8—2981no—
119C4⋊C8—2981no—
120C4⋊C8—1491no—
121C4⋊C8—1491no—
122C4⋊C8C2×D14911yescharacteristic
123C4⋊C8C2×D14911yescharacteristic
124#41—5962no—
125#41—5962no—
126C2×Q8—2981no—
127C2×D4—21no—
128C2×D4—21no—
129C2×D4—2982no—
130C2×D4C4×D14912yes—
131C22×C4—2982no—
132C22×C4—1491no—
133C22×C4—1491no—
134C22×C4—1491no—
135M16—5962no—
136C2×C8—21no—
137C2×C8—21no—
138C2×C8—2981no—
139C2×C8—2981no—
140C2×C8—5962no—
141C4⋊C4—2981no—
142C4⋊C4—1492no—
143C22⋊C4—2982no—
144C22⋊C4—2982no—
145C42—1491no—
146C42—1491no—
147C42—1491no—
148C42C22×D14911yescharacteristic
149C23—22no—
150C23—1491no—
151Q8—5961no—
152Q8—5961no—
153D4—42no—
154D4—41no—
155D4—41no—
156D4—41no—
157D4—41no—
158D4—5964no—
159C2×C4—2981no—
160C2×C4—2981no—
161C2×C4—2982no—
162C2×C4—5961no—
163C2×C4—5964no—
164C2×C4—1491no—
165C2×C4—1491no—
166C2×C4—1491no—
167C2×C4—1492no—
168C2×C4—1492no—
169C2×C4C2×C4×D14911yescharacteristic
170C2×C4D4×D14911yescharacteristic
171C2×C4D4×D14911yescharacteristic
172C8—41no—
173C8—41no—
174C8—5961no—
175C8—5961no—
176C22—42no—
177C22—42no—
178C22—42no—
179C22—2981no—
180C22—2981no—
181C22—1492no—
182C22C22⋊C4×D14911yescharacteristic
183C4—21no—
184C4—2981no—
185C4—2981no—
186C4—5962no—
187C4—1492no—
188C4D8×D14911yescharacteristic
189C4SD16×D14911yescharacteristic
190C4#1801193511yescharacteristic
191C4#1801194011yescharacteristic
192C2—82no—
193C2—2982no—
194C2#2374960611yescharacteristic
195C2#102×D14911yescharacteristic
196C2#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#1547
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. #23749647C2semidirect
3. C4⋊C8×D149C2semidirect
4. #23749372C2semidirect
5. #23749370C2semidirect
6. #23749369C2semidirect
7. #331×C149C2semidirect
98. C149#1547semidirect
106. #331D149semidirect

Maximal subgroups

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

subgroupindex
#237501732
#237496472
C4⋊C8×D1492
#237493722
#237493702
#237493692
#331×C1492
#1547149