Finite Group Databasebeta

← #34060128

Subgroups — #34060128

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#23750477C214yesmaximal, complemented
4C2×#18011886C211yesmaximal, characteristic
5C2×D149⋊C8—21no—
6C2×C4⋊#10597010—21no—
7C2×C22⋊#10597010—21no—
8#18011968C2212yescomplemented
9C22⋊#11924753—21no—
10(C2×#10597010)⋊C4C2212yescomplemented
11C22×D596—21no—
12C22×D596C411yescharacteristic, complemented
13C22×C4×D149C2211yescharacteristic
14#18011886—21no—
15#18011886—21no—
16#18011886C412yescomplemented
17#18011886C2212yes—
18C2×#14558713—21no—
19C2×C4⋊C4×C149C411yescharacteristic, complemented
20C22×#10597010—22no—
21D149⋊C8—42no—
22C2×#11924753—22no—
23C4⋊#10597010—42no—
24C22⋊#10597010—42no—
25C23×D149—21no—
26C23×D149D411yescharacteristic
27C2×D596—22no—
28C2×D596—22no—
29C2×D596—21no—
30C2×D596—42no—
31C2×D596—42no—
32C2×D596—42no—
33C2×D596C2×C412yes—
34C22×Dic149D411yescharacteristic
35C2×C4×D149—42no—
36C2×C4×D149C2×C411yescharacteristic
37C2×C4×D149D411yescharacteristic
38C2×C4×D149D411yescharacteristic
39C2×C4×D149C2311yescharacteristic
40#14558713—22no—
41#14558713—22no—
42C22×C4×C149—21no—
43C22×C4×C149C2×C411yescharacteristic
44C4⋊C4×C149—21no—
45C4⋊C4×C149C2×C412yes—
46C2×#10597010—42no—
47C2×#10597010—42no—
48C2×#10597010—42no—
49#11924753—42no—
50C22×D149—22no—
51C22×D149—41no—
52C22×D149—41no—
53C22×D149—42no—
54C22×D149—42no—
55C22×D149—42no—
56C22×D149C22⋊C411yescharacteristic
57C22×D149D812yes—
58C22×D149SD1612yes—
59C22×D149C2×D411yescharacteristic
60D596—42no—
61D596—44no—
62D596—42no—
63D596—42no—
64D596—42no—
65C2×Dic149—41no—
66C2×Dic149C22⋊C411yescharacteristic
67C2×Dic149C2×D411yescharacteristic
68C4×D149—22no—
69C4×D149—22no—
70C4×D149—41no—
71C4×D149—41no—
72C23×C149C22⋊C411yescharacteristic
73C2×C4×C149—22no—
74C2×C4×C149—22no—
75C2×C4×C149—42no—
76C2×C4×C149C22⋊C411yescharacteristic
77C2×C4×C149C22×C411yescharacteristic
78C22×C149—21no—
79C22×C149—21no—
80C22×C149#10212yes—
81C22×C149C2×C22⋊C411yescharacteristic
82C2×D149—21no—
83C2×D149—21no—
84C2×D149—21no—
85C2×D149—21no—
86C2×D149—42no—
87C2×D149—42no—
88C2×D149—42no—
89C2×D149—42no—
90C2×D149—42no—
91C2×D149—84no—
92C2×D149#10212yes—
93C2×D149C2×D811yescharacteristic
94C2×D149C2×SD1611yescharacteristic
95#10597010—82no—
96C4×C149—21no—
97C4×C149—42no—
98C4×C149#9912yes—
99Dic149—21no—
100Dic149—21no—
101C2×C149—22no—
102C2×C149C2×#9911yescharacteristic
103C2×C149C2×#10211yescharacteristic
104C2×C149#42111yescharacteristic
105D149—21no—
106D149—22no—
107D149—21no—
108D149—82no—
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—1491no—
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#1059701011yescharacteristic, complemented
125C2×C22⋊C4—2981no—
126C2×C22⋊C4—2981no—
127C22⋊C8—2981no—
128C22⋊C8—1492no—
129#95—1492no—
130C24—2981no—
131C24—1491no—
132C2×D4—2982no—
133C2×D4—2982no—
134C2×D4—2981no—
135C2×D4—5962no—
136C2×D4—5962no—
137C2×D4—5962no—
138C2×D4—1492no—
139C22×C4—21no—
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—21no—
151C4⋊C4—5962no—
152C4⋊C4C2×#1059701012yes—
153C22⋊C4—2982no—
154C22⋊C4—2982no—
155C22⋊C4—5962no—
156C23—2982no—
157C23—5961no—
158C23—5961no—
159C23—5962no—
160C23—5962no—
161C23—5962no—
162C23—1491no—
163C23—1491no—
164C23—1492no—
165C23—1492no—
166C23C22⋊#1059701011yescharacteristic
167D4—5962no—
168D4—5962no—
169D4—5964no—
170D4—5962no—
171D4—5962no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—42no—
175C2×C4—2982no—
176C2×C4—2982no—
177C2×C4—5961no—
178C2×C4—5961no—
179C2×C4—5961no—
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—2981no—
191C22—2981no—
192C22—2981no—
193C22—2981no—
194C22—5962no—
195C22—5962no—
196C22—5962no—
197C22—5962no—
198C22—5962no—
199C22—1491no—
200C22—1492no—
201C22—1491no—
202C22—11924no—
203C22#1801197312yes—
204C22C2×C22⋊#1059701011yescharacteristic
205C4—21no—
206C4—42no—
207C4—2981no—
208C4—2981no—
209C4—11922no—
210C4#1801197012yes—
211C2—22no—
212C2—2981no—
213C2—2981no—
214C2—2982no—
215C2—11922no—
216C2C2×#1801197011yescharacteristic
217C2C2×#1801197311yescharacteristic
218C2#2375062411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC2×C4⋊C4×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC2×#18011886C2
cosocleC2×C4×D149C23
hypercenterC2×C4⋊C4#10597010
hypocenterC149#1519
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. D149⋊(C22⋊C8)C2semidirect
2. #23750567C2semidirect
3. #23750477C2semidirect
8. #18011968C22semidirect
10. (C2×#10597010)⋊C4C22semidirect
12. C22×D596C4semidirect
16. #18011886C4semidirect
19. C2×C4⋊C4×C149C4semidirect
109. C149#1519semidirect
124. C2×C4⋊C4#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
#237504772
C2×#180118862
#1519149