Finite Group Databasebeta

← #34060081

Subgroups — #34060081

Order 19072.

272 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 58 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#23750648C211yesmaximal, characteristic, complemented
2#23750561C211yesmaximal, characteristic, complemented
3#23750477C212yesmaximal, complemented
4#23750476C212yesmaximal, complemented
5#23750172C211yesmaximal, characteristic
6C2×C4×#10597010—21no—
7#18011978—21no—
8#18011968C2212yes—
9#18011966—21no—
10(C2×#10597010)⋊C4—21no—
11(C2×#10597010)⋊C4C2212yes—
12C2×#14558736—21no—
13#18011910C411yescharacteristic, complemented
14#18011907C411yescharacteristic, complemented
15#18011897—21no—
16#18011886C2211yescharacteristic
17#18011884—21no—
18#18011882C2211yescharacteristic
19C4×D596C411yescharacteristic, complemented
20C4×C22⋊D149—21no—
21C42×D149C2211yescharacteristic
22C4×D4×C149C411yescharacteristic, complemented
23C22×#10597010—22no—
24C2×#11924753—22no—
25C4×#10597010—24no—
26#14558736—44no—
27C2×Dic298—21no—
28C2×D596—21no—
29C2×D596C2×C411yescharacteristic
30C2×C22⋊D149—21no—
31C2×C22⋊D149—21no—
32C2×C22⋊D149—21no—
33C2×C4×D149—21no—
34C2×C4×D149D411yescharacteristic
35C2×C4×D149D411yescharacteristic
36C2×C4×D149C2311yescharacteristic
37C4⋊Dic149C2×C411yescharacteristic
38#14558715—21no—
39C22⋊Dic149—21no—
40#14558713—21no—
41#14558713—21no—
42C4×Dic149C2×C411yescharacteristic
43C4×Dic149D411yescharacteristic
44C4×Dic149D411yescharacteristic
45C2×D4×C149C2×C411yescharacteristic
46C22×C4×C149—21no—
47C4⋊C4×C149C2×C411yescharacteristic
48C22⋊C4×C149—21no—
49C42×C149C2×C411yescharacteristic
50C2×#10597010—24no—
51C2×#10597010—42no—
52C2×#10597010—42no—
53#11924753—42no—
54C22×D149—21no—
55C22×D149C2×D411yescharacteristic
56Dic298—42no—
57D596—41no—
58D596—42no—
59C22⋊D149—42no—
60C22⋊D149—42no—
61C22⋊D149—42no—
62C2×Dic149—21no—
63C2×Dic149C22⋊C411yescharacteristic
64C2×Dic149C22⋊C411yescharacteristic
65C2×Dic149C2×D411yescharacteristic
66C4×D149—22no—
67C4×D149—22no—
68C4×D149—41no—
69C4×D149—42no—
70C23×C149—21no—
71D4×C149—41no—
72C2×C4×C149—21no—
73C2×C4×C149—42no—
74C2×C4×C149C22⋊C411yescharacteristic
75C2×C4×C149C22⋊C411yescharacteristic
76C2×C4×C149C22×C411yescharacteristic
77C22×C149—41no—
78C22×C149—41no—
79C22×C149—41no—
80C22×C149C2×C22⋊C411yescharacteristic
81C2×D149—21no—
82C2×D149—21no—
83C2×D149—41no—
84C2×D149—41no—
85C2×D149—41no—
86C2×D149AGL(1,ℤ/8)12yes—
87#10597010—44no—
88C4×C149—21no—
89C4×C149—21no—
90C4×C149—21no—
91C4×C149—41no—
92Dic149—21no—
93Dic149—21no—
94Dic149—41no—
95Dic149#10412yes—
96C2×C149—81no—
97C2×C149#41011yescharacteristic
98C2×C149#41811yescharacteristic
99C2×C149C2×#10411yescharacteristic
100D149—22no—
101D149—81no—
102C149#150511yescharacteristic, complemented, Sylow
103#1505—1491nomaximal, Sylow
104#532—1491no—
105#432—1491no—
106#376—1491no—
107#327—1492no—
108#327—1492no—
109C2×#41—2981no—
110C4⋊Q8—1491no—
111#127—1491no—
112#124—2981no—
113#121—2981no—
114#121—1491no—
115#121—1491no—
116C4×D4—2981no—
117C4×D4—1491no—
118C4×D4#1059701011yescharacteristic, complemented
119C2×C42—2981no—
120C2×C42—1491no—
121C4⋊C8—2981no—
122C22⋊C8—1492no—
123#97—2981no—
124#95—2981no—
125#95—1492no—
126#41—5964no—
127C2×Q8—2981no—
128C2×D4—2981no—
129C2×D4—2981no—
130C2×D4—2981no—
131C2×D4—2981no—
132C2×D4—1491no—
133C2×D4C2×#1059701011yescharacteristic
134C22×C4—21no—
135C22×C4—2982no—
136C22×C4—2981no—
137C22×C4—1491no—
138C22×C4—1491no—
139C22×C4—1491no—
140C2×C8—2982no—
141C4⋊C4—2981no—
142C4⋊C4—1491no—
143C4⋊C4C2×#1059701011yescharacteristic
144C22⋊C4—21no—
145C22⋊C4—2981no—
146C22⋊C4—2981no—
147C22⋊C4—2981no—
148C42—2984no—
149C42—1491no—
150C42—1491no—
151C42—1491no—
152C42C2×#1059701011yescharacteristic
153C23—21no—
154C23—2981no—
155C23—1491no—
156Q8—5962no—
157D4—41no—
158D4—5961no—
159D4—5962no—
160D4—5962no—
161D4—5962no—
162D4—5962no—
163C2×C4—21no—
164C2×C4—42no—
165C2×C4—2982no—
166C2×C4—2982no—
167C2×C4—2984no—
168C2×C4—2981no—
169C2×C4—5961no—
170C2×C4—5962no—
171C2×C4—5962no—
172C2×C4—5962no—
173C2×C4—1491no—
174C2×C4—1491no—
175C2×C4—1491no—
176C2×C4C22⋊#1059701011yescharacteristic
177C2×C4C22⋊#1059701011yescharacteristic
178C2×C4C22×#1059701011yescharacteristic
179C8—5962no—
180C22—41no—
181C22—41no—
182C22—41no—
183C22—2981no—
184C22—2981no—
185C22—5961no—
186C22—5961no—
187C22—5961no—
188C22—1492no—
189C22C2×C22⋊#1059701011yescharacteristic
190C4—21no—
191C4—21no—
192C4—21no—
193C4—41no—
194C4—2981no—
195C4—2981no—
196C4—5964no—
197C4—5961no—
198C4—1492no—
199C2—81no—
200C2—2982no—
201C2—11921no—
202C2#2375060411yescharacteristic
203C2#2375061711yescharacteristic
204C2D149⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC4×D4×C149C4
socleC22×C149C2×C22⋊C4
prime radical#23750172C2
cosocleC2×C4×D149C23
hypercenterC4×D4#10597010
hypocenterC149#1505
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #23750648C2semidirect
2. #23750561C2semidirect
3. #23750477C2semidirect
4. #23750476C2semidirect
13. #18011910C4semidirect
14. #18011907C4semidirect
19. C4×D596C4semidirect
22. C4×D4×C149C4semidirect
102. C149#1505semidirect
118. C4×D4#10597010semidirect

Maximal subgroups

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

subgroupindex
#237506482
#237505612
#237504772
#237504762
#237501722
#1505149