Finite Group Databasebeta

← #34060028

Subgroups — #34060028

Order 19072.

266 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 66 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#23750628C211yesmaximal, characteristic, complemented
2C4×#14558745C211yesmaximal, characteristic, complemented
3#23750475C212yesmaximal, complemented
4#23750473C212yesmaximal, complemented
5#23750093C211yesmaximal, characteristic
6C2×#14558745—21no—
7C2×#14558745—21no—
8#18011978—21no—
9C4⋊#11924753C2212yes—
10#18011966—21no—
11C4×#11924753C2212yes—
12C2×#14558736C411yescharacteristic
13#18011876C411yescharacteristic
14#18011876C2211yescharacteristic
15#18011873C411yescharacteristic
16#18011873C2211yescharacteristic
17#18011871—21no—
18#18011871—21no—
19#18011868—21no—
20C2×C4×Dic149C2211yescharacteristic
21C42×D149—21no—
22#117×C149C411yescharacteristic
23#14558745—24no—
24#14558745—42no—
25C2×#11924753—22no—
26C2×#11924753—22no—
27#14558736—22no—
28#14558736—22no—
29C2×Dic298C2×C411yescharacteristic
30C2×D596C2×C411yescharacteristic
31C2×C22⋊D149—21no—
32C22×Dic149D411yescharacteristic
33C22×Dic149D411yescharacteristic
34C2×C4×D149—21no—
35C2×C4×D149—21no—
36C2×C4×D149—21no—
37#14558715—21no—
38#14558715—21no—
39#14558713—21no—
40#14558713—21no—
41C4×Dic149—21no—
42C4×Dic149—21no—
43C4×Dic149C2×C411yescharacteristic
44C4×Dic149D411yescharacteristic
45C4×Dic149D411yescharacteristic
46C4×Dic149C2311yescharacteristic
47C22×C4×C149C2×C411yescharacteristic
48C4⋊C4×C149C2×C411yescharacteristic
49C4⋊C4×C149C2×C411yescharacteristic
50C22⋊C4×C149—21no—
51C42×C149—21no—
52#11924753—24no—
53#11924753—42no—
54C22×D149—21no—
55Dic298—21no—
56Dic298M1612yescomplemented
57D596—21no—
58D596M1612yescomplemented
59C22⋊D149—24no—
60C2×Dic149—21no—
61C2×Dic149—22no—
62C2×Dic149—21no—
63C2×Dic149—21no—
64C2×Dic149C22⋊C411yescharacteristic
65C2×Dic149C22⋊C411yescharacteristic
66C2×Dic149C2×D411yescharacteristic
67C2×Dic149C2×D411yescharacteristic
68C4×D149—24no—
69C4×D149—42no—
70C4×D149—41no—
71C4×D149—41no—
72C23×C149C22⋊C411yescharacteristic
73C2×C4×C149—21no—
74C2×C4×C149—21no—
75C2×C4×C149—21no—
76C2×C4×C149—21no—
77C2×C4×C149C22⋊C411yescharacteristic
78C2×C4×C149C22×C411yescharacteristic
79C22×C149—21no—
80C22×C149—21no—
81C22×C149—21no—
82C22×C149C2×C22⋊C411yescharacteristic
83C2×D149—22no—
84C2×D149—41no—
85C2×D149—41no—
86C4×C149—21no—
87C4×C149—41no—
88C4×C149—41no—
89C4×C149C2×M1611yescharacteristic
90C4×C149C2×M1611yescharacteristic
91Dic149—22no—
92Dic149—21no—
93Dic149—21no—
94Dic149#10412yes—
95Dic149AGL(1,ℤ/8)11yescharacteristic
96Dic149#13711yescharacteristic
97C2×C149—41no—
98C2×C149#40711yescharacteristic
99C2×C149#41711yescharacteristic
100C2×C149C2×#10411yescharacteristic
101D149—42no—
102C149#148911yescharacteristic, complemented, Sylow
103#1489—1491nomaximal, Sylow
104C4×#41—1491no—
105#423—1491no—
106C4×M16—1491no—
107Q8⋊C8—1492no—
108D4⋊C8—1492no—
109C2×#41—1491no—
110C2×M16—2981no—
111C2×M16—2981no—
112C4×Q8—1491no—
113C4×Q8—1491no—
114C4×D4—2981no—
115C4×D4—2981no—
116C4×D4—1491no—
117C4×D4—1491no—
118#117—2981no—
119#117#1059701011yescharacteristic
120C2×C42—2981no—
121C2×C42—1491no—
122C4⋊C8—2981no—
123C4⋊C8—1492no—
124#97—2981no—
125C4×C8—1492no—
126#41—2982no—
127#41—2982no—
128C2×Q8—1491no—
129C2×D4—2981no—
130C2×D4—1491no—
131C22×C4—2981no—
132C22×C4—2981no—
133C22×C4—2981no—
134C22×C4—1491no—
135C22×C4—1491no—
136C22×C4C2×#1059701011yescharacteristic
137M16—2984no—
138M16—5962no—
139C2×C8—2982no—
140C2×C8—2982no—
141C4⋊C4—2981no—
142C4⋊C4—2981no—
143C4⋊C4C2×#1059701011yescharacteristic
144C4⋊C4C2×#1059701011yescharacteristic
145C22⋊C4—21no—
146C22⋊C4—2981no—
147C22⋊C4—2981no—
148C42—21no—
149C42—2981no—
150C42—2981no—
151C42—1491no—
152C42—1491no—
153C42—1491no—
154C42—1491no—
155C23—2981no—
156C23C22⋊#1059701011yescharacteristic
157Q8—2981no—
158Q8—1492no—
159D4—2984no—
160D4—2981no—
161D4—1492no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—2984no—
167C2×C4—2981no—
168C2×C4—2982no—
169C2×C4—2981no—
170C2×C4—2981no—
171C2×C4—5961no—
172C2×C4—5961no—
173C2×C4—5962no—
174C2×C4—1491no—
175C2×C4—1491no—
176C2×C4—1491no—
177C2×C4—1491no—
178C2×C4C22⋊#1059701011yescharacteristic
179C2×C4C22×#1059701011yescharacteristic
180C8—2984no—
181C8—5962no—
182C22—21no—
183C22—21no—
184C22—21no—
185C22—2982no—
186C22—5961no—
187C22—5961no—
188C22C2×C22⋊#1059701011yescharacteristic
189C4—21no—
190C4—41no—
191C4—41no—
192C4—2982no—
193C4—2981no—
194C4—2981no—
195C4—1491no—
196C4—1491no—
197C4—1492no—
198C4D149⋊M1611yescharacteristic
199C4D149⋊M1611yescharacteristic
200C2—41no—
201C2—5962no—
202C2#2375059711yescharacteristic
203C2#2375061611yescharacteristic
204C2D149⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
Fitting#117×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC2×#14558736C4
cosocleC4×Dic149C23
hypercenter#117#10597010
hypocenterC149#1489
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #23750628C2semidirect
2. C4×#14558745C2semidirect
3. #23750475C2semidirect
4. #23750473C2semidirect
56. Dic298M16semidirect
58. D596M16semidirect
102. C149#1489semidirect

Maximal subgroups

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

subgroupindex
#237506282
C4×#145587452
#237504752
#237504732
#237500932
#1489149