Finite Group Databasebeta

← #34060009

Subgroups — #34060009

Order 19072.

234 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 62 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⋊(C4⋊C8)C211yesmaximal, characteristic, complemented
2C4×#14558746C211yesmaximal, characteristic, complemented
3#23750475C212yesmaximal, complemented
4#23750473C212yesmaximal, complemented
5#23750160C211yesmaximal, characteristic
6C2×#14558746—21no—
7C2×D149⋊C8—21no—
8#18011978—21no—
9C4⋊#11924753C2212yes—
10#18011966—21no—
11C4×#11924753C2212yes—
12#18011906—21no—
13#18011899C411yescharacteristic
14#18011896—21no—
15#18011891C411yescharacteristic
16#18011886C411yescharacteristic
17#18011876C2211yescharacteristic
18#18011873—21no—
19#18011873C2211yescharacteristic
20#18011869—21no—
21C42×D149C2211yescharacteristic
22#125×C149C411yescharacteristic
23#14558746—24no—
24D149⋊C8—42no—
25C2×#11924753—22no—
26C2×#11924753—22no—
27C2×Dic298C2×C411yescharacteristic
28C2×D596—21no—
29C2×D596C2×C411yescharacteristic
30C2×C4×D149—21no—
31C2×C4×D149C2×C411yescharacteristic
32C2×C4×D149D411yescharacteristic
33C2×C4×D149D411yescharacteristic
34C4⋊Dic149—21no—
35#14558715—21no—
36#14558713—21no—
37#14558713—21no—
38#14558713—21no—
39#14558713—21no—
40#14558713—21no—
41C4×Dic149—21no—
42C4×Dic149D411yescharacteristic
43C4×Dic149D411yescharacteristic
44C4×Dic149C2311yescharacteristic
45C4⋊C4×C149—21no—
46C4⋊C4×C149—21no—
47C4⋊C4×C149C2×C411yescharacteristic
48C4⋊C4×C149C2×C411yescharacteristic
49C42×C149C2×C411yescharacteristic
50#11924753—24no—
51#11924753—42no—
52C22×D149—21no—
53C22×D149C22⋊C411yescharacteristic
54Dic298—22no—
55D596—22no—
56D596—42no—
57C2×Dic149—21no—
58C2×Dic149C22⋊C411yescharacteristic
59C2×Dic149C2×D411yescharacteristic
60C2×Dic149C2×D411yescharacteristic
61C4×D149—22no—
62C4×D149—22no—
63C4×D149—21no—
64C4×D149—21no—
65C4×D149—41no—
66C4×D149—41no—
67C2×C4×C149—21no—
68C2×C4×C149—21no—
69C2×C4×C149C22⋊C411yescharacteristic
70C2×C4×C149C22⋊C411yescharacteristic
71C2×C4×C149C22×C411yescharacteristic
72C22×C149C2×C22⋊C411yescharacteristic
73C2×D149—21no—
74C2×D149—21no—
75C2×D149—41no—
76C2×D149—41no—
77C2×D149—41no—
78C2×D149#10412yes—
79C4×C149—21no—
80C4×C149—21no—
81C4×C149—41no—
82C4×C149—41no—
83C4×C149#13112yes—
84Dic149—21no—
85Dic149—21no—
86Dic149—41no—
87Dic149AGL(1,ℤ/8)11yescharacteristic
88Dic149#13711yescharacteristic
89C2×C149#40811yescharacteristic
90C2×C149#41711yescharacteristic
91C2×C149C2×#10411yescharacteristic
92D149—22no—
93D149—81no—
94C149#148311yescharacteristic, complemented, Sylow
95#1483—1491nomaximal, Sylow
96#529—1491no—
97C2×C4⋊C8—1491no—
98C4×M16—1491no—
99Q8⋊C8—1492no—
100D4⋊C8—1492no—
101C2×M16—2981no—
102C22×C8—2981no—
103#126—2981no—
104#125#1059701011yescharacteristic
105#124—1491no—
106#123—2981no—
107C22⋊Q8—1491no—
108#121—1491no—
109C4×Q8—1491no—
110C4×D4—2981no—
111C4×D4—1491no—
112#117—2981no—
113C2×C42—1491no—
114C4⋊C8—2981no—
115C4⋊C8—1492no—
116#97—2981no—
117C4×C8—1492no—
118C2×Q8—1491no—
119C2×D4—2981no—
120C2×D4—1491no—
121C22×C4—2981no—
122C22×C4—1491no—
123C22×C4—1491no—
124C22×C4—1491no—
125M16—2984no—
126C2×C8—2982no—
127C2×C8—2982no—
128C2×C8—5962no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—2981no—
132C4⋊C4—2981no—
133C4⋊C4C2×#1059701011yescharacteristic
134C4⋊C4C2×#1059701011yescharacteristic
135C22⋊C4—2981no—
136C22⋊C4—2981no—
137C22⋊C4—2981no—
138C22⋊C4—2981no—
139C22⋊C4—2981no—
140C42—2981no—
141C42—1491no—
142C42—1491no—
143C42—1491no—
144C42C2×#1059701011yescharacteristic
145C23—2981no—
146C23—1491no—
147Q8—2982no—
148D4—2982no—
149D4—5962no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—2982no—
153C2×C4—2981no—
154C2×C4—2981no—
155C2×C4—2982no—
156C2×C4—2981no—
157C2×C4—5961no—
158C2×C4—5961no—
159C2×C4—1491no—
160C2×C4—1491no—
161C2×C4—1491no—
162C2×C4C22⋊#1059701011yescharacteristic
163C2×C4C22⋊#1059701011yescharacteristic
164C2×C4C22×#1059701011yescharacteristic
165C8—2984no—
166C8—5962no—
167C22—2981no—
168C22—2981no—
169C22—5961no—
170C22—5961no—
171C22—5961no—
172C22—1492no—
173C22C2×C22⋊#1059701011yescharacteristic
174C4—21no—
175C4—21no—
176C4—41no—
177C4—41no—
178C4—2981no—
179C4—2981no—
180C4—5961no—
181C4—1491no—
182C4—1491no—
183C4#1801199912yes—
184C2—2982no—
185C2—11921no—
186C2#2375060011yescharacteristic
187C2#2375061611yescharacteristic
188C2D149⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
Fitting#125×C149C4
socleC22×C149C2×C22⋊C4
prime radical#18011886C4
cosocleC4×Dic149C23
hypercenter#125#10597010
hypocenterC149#1483
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
1. D149⋊(C4⋊C8)C2semidirect
2. C4×#14558746C2semidirect
3. #23750475C2semidirect
4. #23750473C2semidirect
94. C149#1483semidirect

Maximal subgroups

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

subgroupindex
D149⋊(C4⋊C8)2
C4×#145587462
#237504752
#237504732
#237501602
#1483149