Finite Group Databasebeta

← #34043393

Subgroups — #34043393

Order 19072.

242 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 65 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
3#23749677C211yesmaximal, characteristic, complemented
4#23749372C211yesmaximal, characteristic, complemented
5#23749370C211yesmaximal, characteristic, complemented
6#23749369C211yesmaximal, characteristic, complemented
7#331×C149C211yesmaximal, characteristic, complemented
8C2×#14558735—21no—
9#18011911C2211yescharacteristic
10#18011898—21no—
11#18011882—21no—
12#18011882C412yes—
13D4×Dic149—21no—
14D4×Dic149C412yes—
15C42×D149C2211yescharacteristic
16C4⋊#11924746C2211yescharacteristic
17C4⋊#11924746C2211yescharacteristic
18#18011823—21no—
19#18011823—21no—
20#18011821—21no—
21C8×Dic149—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
33C2×#11924746—21no—
34C2×#11924746—21no—
35C4⋊Dic149—21no—
36C4⋊Dic149C2×C412yes—
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—41no—
50Dic298—41no—
51C22⋊D149—44no—
52C2×Dic149—22no—
53C2×Dic149—44no—
54C2×Dic149C22⋊C411yescharacteristic
55C2×Dic149C22⋊C411yescharacteristic
56C2×Dic149C22⋊C411yescharacteristic
57C4×D149—21no—
58C4×D149—21no—
59C4×D149—21no—
60C4×D149—21no—
61C4×D149—41no—
62#11924746—41no—
63#11924746—41no—
64C23×C149—22no—
65D4×C149—42no—
66D4×C149—41no—
67D4×C149—41no—
68D4×C149—41no—
69D4×C149—41no—
70C2×C4×C149C22×C411yescharacteristic
71C2×C4×C149C2×D411yescharacteristic
72C2×C4×C149C2×D411yescharacteristic
73C8×C149—41no—
74C8×C149—41no—
75C22×C149—42no—
76C22×C149—42no—
77C22×C149—42no—
78C22×C149C2×C22⋊C411yescharacteristic
79C2×D149—21no—
80C2×D149—21no—
81C2×D149—21no—
82C4×C149—21no—
83C4×C149#13511yescharacteristic
84C4×C149#13511yescharacteristic
85C4×C149AGL(1,ℤ/8)11yescharacteristic
86C4×C149AGL(1,ℤ/8)11yescharacteristic
87Dic149—21no—
88Dic149—21no—
89Dic149—21no—
90Dic149—42no—
91C2×C149—82no—
92C2×C149#41311yescharacteristic
93C2×C149#41611yescharacteristic
94C2×C149#41811yescharacteristic
95D149—41no—
96C149#155311yescharacteristic, complemented, Sylow
97#1553—1491nomaximal, Sylow
98#532—1491no—
99#432—1491no—
100#431—1491no—
101#332—1491no—
102#332—1491no—
103#331—1491no—
104#331D14911yescharacteristic, complemented
105C2×#41—2981no—
106C4⋊Q8—1491no—
107#127C2×D14911yescharacteristic
108#124—2981no—
109#121—2981no—
110#121—1492no—
111C4×D4—2981no—
112C4×D4—1492no—
113C2×C42—1491no—
114C4⋊C8—1491no—
115C4⋊C8—1491no—
116C4⋊C8C2×D14911yescharacteristic
117C4⋊C8C2×D14911yescharacteristic
118C22⋊C8—2981no—
119C22⋊C8—2981no—
120#97—2981no—
121C4×C8—2981no—
122#41—5962no—
123#41—5962no—
124C2×Q8—2981no—
125C2×D4—21no—
126C2×D4—21no—
127C2×D4—2982no—
128C2×D4C4×D14912yes—
129C22×C4—2982no—
130C22×C4—1491no—
131C22×C4—1491no—
132C22×C4—1491no—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—2981no—
136C2×C8—2981no—
137C4⋊C4—2981no—
138C4⋊C4—1492no—
139C22⋊C4—2982no—
140C22⋊C4—2982no—
141C42—1491no—
142C42—1491no—
143C42—1491no—
144C42C22×D14911yescharacteristic
145C23—22no—
146C23—1491no—
147Q8—5961no—
148Q8—5961no—
149D4—42no—
150D4—41no—
151D4—41no—
152D4—41no—
153D4—41no—
154D4—5964no—
155C2×C4—2981no—
156C2×C4—2981no—
157C2×C4—2981no—
158C2×C4—2981no—
159C2×C4—2982no—
160C2×C4—5961no—
161C2×C4—5964no—
162C2×C4—1491no—
163C2×C4—1491no—
164C2×C4—1491no—
165C2×C4C2×C4×D14911yescharacteristic
166C2×C4D4×D14911yescharacteristic
167C2×C4D4×D14911yescharacteristic
168C8—41no—
169C8—41no—
170C8—5961no—
171C8—5961no—
172C22—42no—
173C22—42no—
174C22—42no—
175C22—2981no—
176C22—2981no—
177C22—2981no—
178C22C22⋊C4×D14911yescharacteristic
179C4—21no—
180C4—2981no—
181C4—2981no—
182C4—2981no—
183C4—5962no—
184C4#1801193011yescharacteristic
185C4#1801193211yescharacteristic
186C4#1801193511yescharacteristic
187C4#1801193811yescharacteristic
188C2—82no—
189C2—5961no—
190C2#2374960611yescharacteristic
191C2#2374961811yescharacteristic
192C2#2374962811yescharacteristic
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#1553
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. #23749677C2semidirect
4. #23749372C2semidirect
5. #23749370C2semidirect
6. #23749369C2semidirect
7. #331×C149C2semidirect
96. C149#1553semidirect
104. #331D149semidirect

Maximal subgroups

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

subgroupindex
#237501732
#237496812
#237496772
#237493722
#237493702
#237493692
#331×C1492
#1553149