Finite Group Databasebeta

← #34060160

Subgroups — #34060160

Order 19072.

256 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 60 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#23750645C211yesmaximal, characteristic, complemented
2C2×#18011966C211yesmaximal, characteristic, complemented
3#23750481C212yesmaximal, complemented
4#23750480C212yesmaximal, complemented
5#23750171C211yesmaximal, characteristic
6C22×#11924753—21no—
7#18011978—21no—
8C22⋊#11924753—21no—
9#18011966—21no—
10#18011966C2212yes—
11#18011966C2212yes—
12C2×#14558736C411yescharacteristic
13#18011909C411yescharacteristic
14#18011907C411yescharacteristic
15#18011900C2211yescharacteristic
16#18011898C2211yescharacteristic
17#18011883—21no—
18#18011883—21no—
19C4×C22⋊D149—21no—
20C4×C22⋊D149—21no—
21C2×C4×Dic149C2211yescharacteristic
22C2×#41×C149C411yescharacteristic
23C2×#11924753—24no—
24C2×#11924753—22no—
25C2×#11924753—22no—
26#14558736—42no—
27C2×Dic298C2×C411yescharacteristic
28C2×D596C2×C411yescharacteristic
29C2×C22⋊D149—21no—
30C2×C22⋊D149—21no—
31C2×C22⋊D149—21no—
32C22×Dic149D411yescharacteristic
33C22×Dic149D411yescharacteristic
34C2×C4×D149—21no—
35#14558715—21no—
36#14558715—21no—
37C22⋊Dic149—21no—
38C22⋊Dic149—21no—
39#14558713—21no—
40#14558713—21no—
41C4×Dic149C2×C411yescharacteristic
42C4×Dic149D411yescharacteristic
43C4×Dic149D411yescharacteristic
44C4×Dic149C2311yescharacteristic
45#41×C149—42no—
46C2×Q8×C149C2×C411yescharacteristic
47C2×D4×C149—21no—
48C2×D4×C149C2×C411yescharacteristic
49C22×C4×C149—21no—
50C22×C4×C149C2×C411yescharacteristic
51#11924753—24no—
52#11924753—42no—
53C22×D149—21no—
54Dic298—41no—
55D596—41no—
56C22⋊D149—42no—
57C22⋊D149—42no—
58C22⋊D149—42no—
59C2×Dic149—22no—
60C2×Dic149—21no—
61C2×Dic149—41no—
62C2×Dic149C22⋊C411yescharacteristic
63C2×Dic149C22⋊C411yescharacteristic
64C2×Dic149C2×D411yescharacteristic
65C2×Dic149C2×D411yescharacteristic
66C4×D149—42no—
67C23×C149—21no—
68C23×C149C22⋊C411yescharacteristic
69Q8×C149—41no—
70D4×C149—41no—
71D4×C149—42no—
72C2×C4×C149—22no—
73C2×C4×C149—21no—
74C2×C4×C149—42no—
75C2×C4×C149C22⋊C411yescharacteristic
76C2×C4×C149C22×C411yescharacteristic
77C22×C149—21no—
78C22×C149—21no—
79C22×C149—41no—
80C22×C149—41no—
81C22×C149—41no—
82C22×C149#10012yes—
83C22×C149C2×C22⋊C411yescharacteristic
84C2×D149—41no—
85C2×D149—41no—
86C2×D149—41no—
87C4×C149—21no—
88C4×C149—21no—
89C4×C149—41no—
90Dic149—21no—
91Dic149—21no—
92Dic149—21no—
93Dic149—41no—
94Dic149#10412yes—
95C2×C149—22no—
96C2×C149—81no—
97C2×C149C2×#10011yescharacteristic
98C2×C149C2×#10411yescharacteristic
99C2×C149#42111yescharacteristic
100D149—81no—
101C149#153011yescharacteristic, complemented, Sylow
102#1530—1491nomaximal, Sylow
103#532—1491no—
104#432—1491no—
105C2×#97—1491no—
106#329—1492no—
107#329—1492no—
108C2×#41—1491no—
109C2×#41#1059701011yescharacteristic
110C22×C8—2981no—
111C4⋊Q8—1491no—
112#127—1491no—
113#124—1491no—
114#124—1491no—
115#121—2981no—
116#121—2981no—
117C4×D4—2981no—
118C4×D4—2981no—
119C2×C42—1491no—
120C4⋊C8—2981no—
121C22⋊C8—2981no—
122#97—2981no—
123#97—1492no—
124#97—1492no—
125#41—42no—
126#41—5962no—
127C2×Q8—1491no—
128C2×Q8C2×#1059701011yescharacteristic
129C2×D4—21no—
130C2×D4—2981no—
131C2×D4—2981no—
132C2×D4—2981no—
133C2×D4—1491no—
134C2×D4C2×#1059701011yescharacteristic
135C22×C4—21no—
136C22×C4—2981no—
137C22×C4—1491no—
138C22×C4—1491no—
139C22×C4C2×#1059701011yescharacteristic
140C2×C8—2984no—
141C2×C8—2982no—
142C2×C8—2982no—
143C4⋊C4—2981no—
144C4⋊C4—2981no—
145C22⋊C4—2981no—
146C22⋊C4—2981no—
147C22⋊C4—2981no—
148C22⋊C4—2981no—
149C42—1491no—
150C42—1491no—
151C42—1491no—
152C42—1491no—
153C23—21no—
154C23—2981no—
155C23C22⋊#1059701011yescharacteristic
156Q8—41no—
157Q8—5961no—
158D4—41no—
159D4—42no—
160D4—5961no—
161D4—5962no—
162D4—5962no—
163D4—5962no—
164C2×C4—22no—
165C2×C4—21no—
166C2×C4—42no—
167C2×C4—2982no—
168C2×C4—2981no—
169C2×C4—5962no—
170C2×C4—5961no—
171C2×C4—1491no—
172C2×C4—1491no—
173C2×C4—1491no—
174C2×C4—1491no—
175C2×C4C22⋊#1059701011yescharacteristic
176C2×C4C22×#1059701011yescharacteristic
177C8—2984no—
178C8—5962no—
179C22—21no—
180C22—21no—
181C22—41no—
182C22—41no—
183C22—41no—
184C22—5961no—
185C22—5961no—
186C22—5961no—
187C22#1801197112yes—
188C22C2×C22⋊#1059701011yescharacteristic
189C4—21no—
190C4—21no—
191C4—41no—
192C4—2981no—
193C4—2981no—
194C4—2981no—
195C4—5961no—
196C4—1492no—
197C2—22no—
198C2—81no—
199C2—11921no—
200C2C2×#1801197111yescharacteristic
201C2D149⋊#10411yescharacteristic
202C2#2375062211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC2×#41×C149C4
socleC22×C149C2×C22⋊C4
prime radical#23750171C2
cosocleC4×Dic149C23
hypercenterC2×#41#10597010
hypocenterC149#1530
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #23750645C2semidirect
2. C2×#18011966C2semidirect
3. #23750481C2semidirect
4. #23750480C2semidirect
101. C149#1530semidirect

Maximal subgroups

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

subgroupindex
#237506452
C2×#180119662
#237504812
#237504802
#237501712
#1530149