Finite Group Databasebeta

← #34060127

Subgroups — #34060127

Order 19072.

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

normal subgroups only

This group has 340 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
1D149⋊(C22⋊C8)C211yesmaximal, characteristic, complemented
2#23750567C211yesmaximal, characteristic, complemented
3#23750476C214yesmaximal, complemented
4C2×#18011882C211yesmaximal, characteristic
5C2×D149⋊C8—21no—
6C2×C4⋊#10597010—21no—
7C2×C22⋊#10597010—21no—
8#18011968C2212yescomplemented
9C22⋊#11924753—21no—
10(C2×#10597010)⋊C4C2212yescomplemented
11C22×C22⋊D149—21no—
12C22×C4×D149C2211yescharacteristic
13#18011882—21no—
14#18011882—21no—
15#18011882C412yescomplemented
16#18011882C2212yes—
17C2×C4⋊Dic149C411yescharacteristic, complemented
18C2×C22⋊Dic149—21no—
19C22×D4×C149C411yescharacteristic, complemented
20C22×#10597010—22no—
21D149⋊C8—42no—
22C2×#11924753—22no—
23C4⋊#10597010—42no—
24C22⋊#10597010—42no—
25C23×D149D411yescharacteristic
26C2×C22⋊D149—22no—
27C2×C22⋊D149—22no—
28C2×C22⋊D149—42no—
29C2×C22⋊D149—42no—
30C22×Dic149—21no—
31C22×Dic149D411yescharacteristic
32C2×C4×D149—42no—
33C2×C4×D149C2×C411yescharacteristic
34C2×C4×D149D411yescharacteristic
35C2×C4×D149D411yescharacteristic
36C2×C4×D149C2311yescharacteristic
37C4⋊Dic149—21no—
38C4⋊Dic149C2×C412yes—
39C22⋊Dic149—22no—
40C22⋊Dic149—22no—
41C24×C149—21no—
42C2×D4×C149—21no—
43C2×D4×C149—42no—
44C2×D4×C149C2×C412yes—
45C22×C4×C149C2×C411yescharacteristic
46C2×#10597010—42no—
47C2×#10597010—42no—
48C2×#10597010—42no—
49#11924753—42no—
50C22×D149—41no—
51C22×D149—41no—
52C22×D149C22⋊C411yescharacteristic
53C22×D149D812yes—
54C22×D149SD1612yes—
55C22×D149C2×D411yescharacteristic
56C22⋊D149—44no—
57C22⋊D149—42no—
58C22⋊D149—42no—
59C2×Dic149—22no—
60C2×Dic149—41no—
61C2×Dic149—42no—
62C2×Dic149C22⋊C411yescharacteristic
63C2×Dic149C2×D411yescharacteristic
64C4×D149—22no—
65C4×D149—22no—
66C4×D149—41no—
67C4×D149—41no—
68C23×C149—22no—
69C23×C149—42no—
70C23×C149—42no—
71C23×C149—42no—
72C23×C149C22⋊C411yescharacteristic
73D4×C149—42no—
74D4×C149—42no—
75C2×C4×C149—22no—
76C2×C4×C149C22⋊C411yescharacteristic
77C2×C4×C149C22×C411yescharacteristic
78C22×C149—21no—
79C22×C149—21no—
80C22×C149—42no—
81C22×C149—42no—
82C22×C149—42no—
83C22×C149—84no—
84C22×C149#10212yes—
85C22×C149C2×C22⋊C411yescharacteristic
86C2×D149—21no—
87C2×D149—21no—
88C2×D149—21no—
89C2×D149—21no—
90C2×D149—42no—
91C2×D149—42no—
92C2×D149#10212yes—
93C2×D149C2×D811yescharacteristic
94C2×D149C2×SD1611yescharacteristic
95#10597010—82no—
96C4×C149—21no—
97C4×C149#9912yes—
98Dic149—21no—
99Dic149—21no—
100Dic149—42no—
101C2×C149—22no—
102C2×C149—82no—
103C2×C149C2×#9911yescharacteristic
104C2×C149C2×#10211yescharacteristic
105C2×C149#42111yescharacteristic
106D149—21no—
107D149—22no—
108D149—21no—
109C149#151911yescharacteristic, complemented, Sylow
110#1519—1491nomaximal, Sylow
111C2×#121—1491no—
112C2×C22⋊C8—1491no—
113#380—1491no—
114#327—1494no—
115C22×D4—2981no—
116C22×D4#1059701011yescharacteristic, complemented
117C23×C4—1491no—
118C22×C8—2981no—
119#121—2981no—
120#121—2981no—
121#121—1492no—
122#121—1492no—
123C2×C4⋊C4—2981no—
124C2×C4⋊C4—1491no—
125C2×C22⋊C4—2981no—
126C2×C22⋊C4—2981no—
127C22⋊C8—2981no—
128C22⋊C8—1492no—
129#95—1492no—
130C24—21no—
131C24—1491no—
132C2×D4—21no—
133C2×D4—42no—
134C2×D4—2982no—
135C2×D4—2982no—
136C2×D4—5962no—
137C2×D4—5962no—
138C2×D4C2×#1059701012yes—
139C22×C4—2981no—
140C22×C4—2982no—
141C22×C4—5962no—
142C22×C4—1491no—
143C22×C4—1491no—
144C22×C4—1491no—
145C22×C4—1491no—
146C22×C4—1491no—
147C22×C4C2×#1059701011yescharacteristic
148C2×C8—2982no—
149C2×C8—5962no—
150C4⋊C4—2981no—
151C4⋊C4—5962no—
152C4⋊C4—1492no—
153C22⋊C4—2982no—
154C22⋊C4—2982no—
155C22⋊C4—5962no—
156C23—22no—
157C23—42no—
158C23—42no—
159C23—42no—
160C23—5961no—
161C23—5961no—
162C23—1491no—
163C23—1491no—
164C23—1492no—
165C23—1492no—
166C23C22⋊#1059701011yescharacteristic
167D4—42no—
168D4—42no—
169D4—5962no—
170D4—5964no—
171D4—5962no—
172C2×C4—22no—
173C2×C4—2982no—
174C2×C4—2982no—
175C2×C4—2982no—
176C2×C4—5961no—
177C2×C4—5961no—
178C2×C4—5961no—
179C2×C4—5962no—
180C2×C4—5962no—
181C2×C4—5962no—
182C2×C4—5962no—
183C2×C4—1491no—
184C2×C4—1491no—
185C2×C4C22⋊#1059701011yescharacteristic
186C2×C4C22×#1059701011yescharacteristic
187C8—5962no—
188C22—21no—
189C22—21no—
190C22—42no—
191C22—42no—
192C22—42no—
193C22—84no—
194C22—2981no—
195C22—2981no—
196C22—2981no—
197C22—2981no—
198C22—5962no—
199C22—5962no—
200C22—1491no—
201C22—1492no—
202C22—1491no—
203C22#1801197312yes—
204C22C2×C22⋊#1059701011yescharacteristic
205C4—21no—
206C4—2981no—
207C4—2981no—
208C4—5962no—
209C4—11922no—
210C4#1801196912yes—
211C2—22no—
212C2—82no—
213C2—2981no—
214C2—2981no—
215C2—2982no—
216C2C2×#1801196911yescharacteristic
217C2C2×#1801197311yescharacteristic
218C2#2375062311yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC22×D4×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC2×#18011882C2
cosocleC2×C4×D149C23
hypercenterC22×D4#10597010
hypocenterC149#1519
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. D149⋊(C22⋊C8)C2semidirect
2. #23750567C2semidirect
3. #23750476C2semidirect
8. #18011968C22semidirect
10. (C2×#10597010)⋊C4C22semidirect
15. #18011882C4semidirect
17. C2×C4⋊Dic149C4semidirect
19. C22×D4×C149C4semidirect
109. C149#1519semidirect
116. C22×D4#10597010semidirect

Maximal subgroups

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

subgroupindex
D149⋊(C22⋊C8)2
#237505672
#237504762
C2×#180118822
#1519149