Finite Group Databasebeta

← #34060091

Subgroups — #34060091

Order 19072.

294 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 64 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#23750596C211yesmaximal, characteristic
2C4×C22⋊#10597010C211yesmaximal, characteristic
3#23750479C214yesmaximal, complemented
4C2×#18011887C211yesmaximal, characteristic
5C2×#14558746—21no—
6C2×C22⋊#10597010—21no—
7C2×C4×#10597010—21no—
8#18011968C2212yes—
9C22⋊#11924753—21no—
10(C2×#10597010)⋊C4C2212yes—
11C22×C4×D149C2211yescharacteristic
12#18011887—21no—
13#18011887—21no—
14#18011887C412yescomplemented
15#18011887C2212yes—
16C2×C4⋊Dic149C411yescharacteristic, complemented
17C2×#14558715—21no—
18C2×#14558713—21no—
19C22×Q8×C149C411yescharacteristic, complemented
20C22×#10597010—22no—
21#14558746—42no—
22C2×#11924753—22no—
23C22⋊#10597010—24no—
24C4×#10597010—42no—
25C23×D149D411yescharacteristic
26C22×Dic149—21no—
27C22×Dic149D411yescharacteristic
28C2×C4×D149—42no—
29C2×C4×D149C2×C411yescharacteristic
30C2×C4×D149D411yescharacteristic
31C2×C4×D149D411yescharacteristic
32C2×C4×D149C2311yescharacteristic
33C4⋊Dic149—21no—
34C4⋊Dic149C2×C412yes—
35#14558715—22no—
36#14558715—22no—
37#14558713—22no—
38#14558713—22no—
39C2×Q8×C149—21no—
40C2×Q8×C149—42no—
41C2×Q8×C149C2×C412yes—
42C22×C4×C149—21no—
43C22×C4×C149C2×C411yescharacteristic
44C2×#10597010—24no—
45C2×#10597010—42no—
46C2×#10597010—42no—
47#11924753—42no—
48C22×D149—22no—
49C22×D149—22no—
50C22×D149—41no—
51C22×D149C22⋊C411yescharacteristic
52C22×D149C2×D411yescharacteristic
53C2×Dic149—22no—
54C2×Dic149—41no—
55C2×Dic149—42no—
56C2×Dic149C22⋊C411yescharacteristic
57C2×Dic149C2×D411yescharacteristic
58C4×D149—22no—
59C4×D149—22no—
60C4×D149—41no—
61C4×D149—41no—
62C23×C149C22⋊C411yescharacteristic
63Q8×C149—42no—
64Q8×C149—42no—
65C2×C4×C149—22no—
66C2×C4×C149—22no—
67C2×C4×C149—42no—
68C2×C4×C149C22⋊C411yescharacteristic
69C2×C4×C149C22×C411yescharacteristic
70C22×C149—21no—
71C22×C149—21no—
72C22×C149#10412yes—
73C22×C149C2×C22⋊C411yescharacteristic
74C2×D149—21no—
75C2×D149—21no—
76C2×D149—21no—
77C2×D149—21no—
78C2×D149—21no—
79C2×D149—44no—
80C2×D149#13712yes—
81#10597010—44no—
82C4×C149—21no—
83C4×C149—42no—
84C4×C149#9912yes—
85Dic149—21no—
86Dic149—21no—
87Dic149—42no—
88C2×C149—22no—
89C2×C149C2×#9911yescharacteristic
90C2×C149#41911yescharacteristic
91C2×C149C2×#10411yescharacteristic
92D149—22no—
93D149—41no—
94C149#150811yescharacteristic, complemented, Sylow
95#1508—1491nomaximal, Sylow
96C2×C22⋊Q8—1491no—
97#407—1491no—
98C4×C22⋊C4—1491no—
99#328—1494no—
100C22×Q8#1059701011yescharacteristic, complemented
101C23×C4—1491no—
102C2×M16—2981no—
103C22⋊Q8—2981no—
104C22⋊Q8—2981no—
105C22⋊Q8—1492no—
106C22⋊Q8—1492no—
107C2×C4⋊C4—2981no—
108C2×C4⋊C4—1491no—
109C2×C22⋊C4—2981no—
110C2×C22⋊C4—2981no—
111C2×C42—2981no—
112C22⋊C8—2981no—
113C22⋊C8—1492no—
114#95—1492no—
115C24—1491no—
116C2×Q8—21no—
117C2×Q8—42no—
118C2×Q8C2×#1059701012yes—
119C22×C4—21no—
120C22×C4—2982no—
121C22×C4—2981no—
122C22×C4—5962no—
123C22×C4—1491no—
124C22×C4—1491no—
125C22×C4—1491no—
126C22×C4—1491no—
127C22×C4—1491no—
128C22×C4C2×#1059701011yescharacteristic
129M16—5962no—
130C2×C8—2982no—
131C4⋊C4—2982no—
132C4⋊C4—2982no—
133C4⋊C4—2981no—
134C4⋊C4—1492no—
135C22⋊C4—2982no—
136C22⋊C4—2982no—
137C22⋊C4—2984no—
138C42—5962no—
139C23—2982no—
140C23—2982no—
141C23—5961no—
142C23—1491no—
143C23—1491no—
144C23C22⋊#1059701011yescharacteristic
145Q8—42no—
146Q8—42no—
147C2×C4—22no—
148C2×C4—22no—
149C2×C4—42no—
150C2×C4—2982no—
151C2×C4—2982no—
152C2×C4—2984no—
153C2×C4—2982no—
154C2×C4—5961no—
155C2×C4—5961no—
156C2×C4—5961no—
157C2×C4—5962no—
158C2×C4—5962no—
159C2×C4—5962no—
160C2×C4—1491no—
161C2×C4—1491no—
162C2×C4C22⋊#1059701011yescharacteristic
163C2×C4C22×#1059701011yescharacteristic
164C8—5962no—
165C22—21no—
166C22—21no—
167C22—2981no—
168C22—2981no—
169C22—2981no—
170C22—2981no—
171C22—2981no—
172C22—5964no—
173C22—1492no—
174C22#1801197612yes—
175C22C2×C22⋊#1059701011yescharacteristic
176C4—21no—
177C4—42no—
178C4—2981no—
179C4—2981no—
180C4—5964no—
181C4—5962no—
182C4#1801196912yes—
183C2—22no—
184C2—2982no—
185C2—5961no—
186C2C2×#1801196911yescharacteristic
187C2#2375061811yescharacteristic
188C2C2×#1801197611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC22×Q8×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC23×D149D4
cosocleC2×C4×D149C23
hypercenterC22×Q8#10597010
hypocenterC149#1508
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
3. #23750479C2semidirect
14. #18011887C4semidirect
16. C2×C4⋊Dic149C4semidirect
19. C22×Q8×C149C4semidirect
94. C149#1508semidirect
100. C22×Q8#10597010semidirect

Maximal subgroups

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

subgroupindex
#237505962
C4×C22⋊#105970102
#237504792
C2×#180118872
#1508149