Finite Group Databasebeta

← #34060143

Subgroups — #34060143

Order 19072.

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

normal subgroups only

This group has 234 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
1C4×#14558746C211yesmaximal, characteristic, complemented
2#23750584C211yesmaximal, characteristic, complemented
3#23750482C212yesmaximal, complemented
4#23750481C212yesmaximal, complemented
5#23750162C211yesmaximal, characteristic
6C2×#14558746—21no—
7C2×D149⋊C8—21no—
8#18011966—21no—
9#18011966C2212yes—
10#18011966C2212yes—
11C4×#11924753—21no—
12#18011906—21no—
13#18011902C2211yescharacteristic
14#18011900C2211yescharacteristic
15#18011896—21no—
16#18011887C411yescharacteristic
17#18011886C411yescharacteristic
18C4×D596—21no—
19C4×D596C411yescharacteristic
20#18011868—21no—
21C42×D149C2211yescharacteristic
22C4×Q8×C149C411yescharacteristic
23#14558746—24no—
24D149⋊C8—24no—
25C2×#11924753—22no—
26C2×#11924753—22no—
27C2×D596—21no—
28C2×D596C2×C411yescharacteristic
29C2×C4×D149—21no—
30C2×C4×D149C2×C411yescharacteristic
31C2×C4×D149D411yescharacteristic
32C2×C4×D149D411yescharacteristic
33C4⋊Dic149—21no—
34C4⋊Dic149C2×C411yescharacteristic
35#14558715—21no—
36#14558715—21no—
37#14558713—21no—
38#14558713—21no—
39#14558713—21no—
40#14558713—21no—
41#14558713—21no—
42C4×Dic149D411yescharacteristic
43C4×Dic149D411yescharacteristic
44C4×Dic149C2311yescharacteristic
45C2×Q8×C149C2×C411yescharacteristic
46C4⋊C4×C149—21no—
47C4⋊C4×C149C2×C411yescharacteristic
48C42×C149—21no—
49C42×C149C2×C411yescharacteristic
50#11924753—24no—
51#11924753—24no—
52C22×D149—21no—
53C22×D149C22⋊C411yescharacteristic
54D596—41no—
55D596—42no—
56C2×Dic149—21no—
57C2×Dic149C22⋊C411yescharacteristic
58C2×Dic149C2×D411yescharacteristic
59C2×Dic149C2×D411yescharacteristic
60C4×D149—22no—
61C4×D149—22no—
62C4×D149—41no—
63C4×D149—42no—
64Q8×C149—41no—
65C2×C4×C149—21no—
66C2×C4×C149—21no—
67C2×C4×C149C22⋊C411yescharacteristic
68C2×C4×C149C22⋊C411yescharacteristic
69C2×C4×C149C22×C411yescharacteristic
70C22×C149C2×C22⋊C411yescharacteristic
71C2×D149—21no—
72C2×D149—21no—
73C2×D149—41no—
74C2×D149—41no—
75C2×D149—41no—
76C2×D149#10412yes—
77C4×C149—21no—
78C4×C149—21no—
79C4×C149—41no—
80C4×C149—41no—
81C4×C149#10412yes—
82Dic149—21no—
83Dic149—21no—
84Dic149—21no—
85Dic149—41no—
86C2×C149#41311yescharacteristic
87C2×C149C2×#10411yescharacteristic
88C2×C149C2×#10411yescharacteristic
89D149—22no—
90D149—81no—
91C149#152411yescharacteristic, complemented, Sylow
92#1524—1491nomaximal, Sylow
93#529—1491no—
94C4×M16—1491no—
95C2×#97—1491no—
96#330—1492no—
97#329—1492no—
98C2×M16—2981no—
99C22×C8—2981no—
100#126—2981no—
101#125—1491no—
102#124—1491no—
103#123—2981no—
104C22⋊Q8—1491no—
105#121—1491no—
106C4×Q8#1059701011yescharacteristic
107C4×D4—2981no—
108C4×D4—1491no—
109#117—2981no—
110C2×C42—1491no—
111#97—2981no—
112#97—1492no—
113#97—1492no—
114C4×C8—2981no—
115C2×Q8C2×#1059701011yescharacteristic
116C2×D4—2981no—
117C2×D4—1491no—
118C22×C4—2981no—
119C22×C4—1491no—
120C22×C4—1491no—
121C22×C4—1491no—
122M16—2984no—
123C2×C8—2984no—
124C2×C8—2982no—
125C2×C8—2982no—
126C4⋊C4—21no—
127C4⋊C4—2981no—
128C4⋊C4—2981no—
129C4⋊C4—2981no—
130C4⋊C4—1491no—
131C4⋊C4C2×#1059701011yescharacteristic
132C22⋊C4—2981no—
133C22⋊C4—2981no—
134C22⋊C4—2981no—
135C22⋊C4—2981no—
136C22⋊C4—2981no—
137C42—21no—
138C42—1491no—
139C42—1491no—
140C42—1491no—
141C42C2×#1059701011yescharacteristic
142C23—2981no—
143C23—1491no—
144Q8—41no—
145D4—5961no—
146D4—5962no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—2982no—
150C2×C4—2982no—
151C2×C4—2981no—
152C2×C4—5961no—
153C2×C4—5962no—
154C2×C4—1491no—
155C2×C4—1491no—
156C2×C4—1491no—
157C2×C4C22⋊#1059701011yescharacteristic
158C2×C4C22⋊#1059701011yescharacteristic
159C2×C4C22×#1059701011yescharacteristic
160C8—2984no—
161C8—2984no—
162C22—2981no—
163C22—2981no—
164C22—5961no—
165C22—5961no—
166C22—5961no—
167C22—1492no—
168C22C2×C22⋊#1059701011yescharacteristic
169C4—21no—
170C4—21no—
171C4—41no—
172C4—41no—
173C4—2981no—
174C4—2981no—
175C4—2981no—
176C4—5961no—
177C4#1801197612yes—
178C2—2982no—
179C2—11921no—
180C2#2375061111yescharacteristic
181C2D149⋊#10411yescharacteristic
182C2C2×#1801197611yescharacteristic
subgroupG/H
centerC2×C4C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC4×Q8×C149C4
socleC22×C149C2×C22⋊C4
prime radical#18011886C4
cosocleC4×Dic149C23
hypercenterC4×Q8#10597010
hypocenterC149#1524
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C4×#14558746C2semidirect
2. #23750584C2semidirect
3. #23750482C2semidirect
4. #23750481C2semidirect
91. C149#1524semidirect

Maximal subgroups

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

subgroupindex
C4×#145587462
#237505842
#237504822
#237504812
#237501622
#1524149