Finite Group Databasebeta

← #34060124

Subgroups — #34060124

Order 19072.

220 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 66 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#23750644C211yesmaximal, characteristic
2#23750569C211yesmaximal, characteristic
3#23750479C212yesmaximal
4#23750478C212yesmaximal
5#23750179C211yesmaximal, characteristic
6C2×C4⋊#10597010—21no—
7C4⋊#11924753—21no—
8#18011968C2212yes—
9C4×#11924753—21no—
10(C2×#10597010)⋊C4—21no—
11(C2×#10597010)⋊C4C2212yes—
12#18011910C411yescharacteristic, complemented
13#18011909C411yescharacteristic, complemented
14#18011901—21no—
15#18011891C2211yescharacteristic
16#18011889—21no—
17#18011887C2211yescharacteristic
18C4×Dic298—21no—
19C4×Dic298C411yescharacteristic, complemented
20#18011868—21no—
21C42×D149C2211yescharacteristic
22C4×Q8×C149C411yescharacteristic, complemented
23C22×#10597010—22no—
24C2×#11924753—22no—
25C4⋊#10597010—42no—
26C2×Dic298—21no—
27C2×Dic298C2×C411yescharacteristic
28C2×C4×D149D411yescharacteristic
29C2×C4×D149D411yescharacteristic
30C2×C4×D149C2311yescharacteristic
31C4⋊Dic149—21no—
32C4⋊Dic149C2×C411yescharacteristic
33#14558715—21no—
34#14558715—21no—
35#14558715—21no—
36#14558715—21no—
37#14558715—21no—
38#14558713—21no—
39#14558713—21no—
40C4×Dic149—21no—
41C4×Dic149C2×C411yescharacteristic
42C4×Dic149D411yescharacteristic
43C4×Dic149D411yescharacteristic
44C2×Q8×C149C2×C411yescharacteristic
45C4⋊C4×C149—21no—
46C4⋊C4×C149C2×C411yescharacteristic
47C42×C149—21no—
48C42×C149C2×C411yescharacteristic
49C2×#10597010—42no—
50C2×#10597010—42no—
51C2×#10597010—42no—
52#11924753—42no—
53C22×D149C2×D411yescharacteristic
54Dic298—42no—
55Dic298—41no—
56C2×Dic149—21no—
57C2×Dic149—21no—
58C2×Dic149C22⋊C411yescharacteristic
59C2×Dic149C22⋊C411yescharacteristic
60C2×Dic149C2×D411yescharacteristic
61C4×D149—41no—
62C4×D149—41no—
63C4×D149SD1612yes—
64C4×D149Q1612yes—
65Q8×C149—41no—
66C2×C4×C149—21no—
67C2×C4×C149—21no—
68C2×C4×C149C22⋊C411yescharacteristic
69C2×C4×C149C22⋊C411yescharacteristic
70C2×C4×C149C22×C411yescharacteristic
71C22×C149C2×C22⋊C411yescharacteristic
72C2×D149—21no—
73C2×D149—21no—
74C2×D149C2×SD1611yescharacteristic
75C2×D149C2×Q1611yescharacteristic
76#10597010—82no—
77C4×C149—21no—
78C4×C149—21no—
79C4×C149—41no—
80C4×C149—41no—
81C4×C149#10312yes—
82Dic149—21no—
83Dic149—21no—
84Dic149—41no—
85Dic149—41no—
86Dic149#10312yes—
87C2×C149#41011yescharacteristic
88C2×C149C2×#10311yescharacteristic
89C2×C149#42111yescharacteristic
90D149—21no—
91D149—21no—
92C149#151811yescharacteristic, complemented, Sylow
93#1518—1491nomaximal, Sylow
94#533—1491no—
95#431—1491no—
96#382—1491no—
97#328—1492no—
98#328—1492no—
99C4⋊Q8—1491no—
100C4⋊Q8—1491no—
101#125—2981no—
102C22⋊Q8—2981no—
103C22⋊Q8—1491no—
104C22⋊Q8—1491no—
105C4×Q8—2981no—
106C4×Q8—1491no—
107C4×Q8#1059701011yescharacteristic, complemented
108#117—2981no—
109C2×C4⋊C4—2981no—
110C2×C42—1491no—
111C4⋊C8—2981no—
112C22⋊C8—1492no—
113C4×C8—2981no—
114#95—2981no—
115#95—1492no—
116C2×Q8—2981no—
117C2×Q8—1491no—
118C2×Q8C2×#1059701011yescharacteristic
119C22×C4—2982no—
120C22×C4—1491no—
121C22×C4—1491no—
122C22×C4—1491no—
123C2×C8—2982no—
124C4⋊C4—21no—
125C4⋊C4—2981no—
126C4⋊C4—2981no—
127C4⋊C4—2981no—
128C4⋊C4—2981no—
129C4⋊C4—2981no—
130C4⋊C4—2981no—
131C4⋊C4—5962no—
132C4⋊C4—1491no—
133C4⋊C4C2×#1059701011yescharacteristic
134C22⋊C4—2981no—
135C22⋊C4—2981no—
136C42—21no—
137C42—2981no—
138C42—1491no—
139C42—1491no—
140C42—1491no—
141C42C2×#1059701011yescharacteristic
142C23—1491no—
143Q8—41no—
144Q8—5961no—
145Q8—5962no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—2981no—
149C2×C4—2981no—
150C2×C4—5961no—
151C2×C4—5961no—
152C2×C4—5962no—
153C2×C4—5962no—
154C2×C4—5962no—
155C2×C4—1491no—
156C2×C4—1491no—
157C2×C4—1491no—
158C2×C4—1492no—
159C2×C4—1492no—
160C2×C4C22⋊#1059701011yescharacteristic
161C2×C4C22⋊#1059701011yescharacteristic
162C2×C4C22×#1059701011yescharacteristic
163C8—5962no—
164C22—2981no—
165C22—2981no—
166C22—1491no—
167C22—1491no—
168C22C2×C22⋊#1059701011yescharacteristic
169C4—21no—
170C4—21no—
171C4—41no—
172C4—41no—
173C4—2981no—
174C4—2981no—
175C4—5961no—
176C4—5961no—
177C4—1492no—
178C4—11922no—
179C4#1801197412yes—
180C2—2981no—
181C2—2981no—
182C2#2375060411yescharacteristic
183C2C2×#1801197411yescharacteristic
184C2#2375062211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC4×Q8×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC22×D149C2×D4
cosocleC2×C4×D149C23
hypercenterC4×Q8#10597010
hypocenterC149#1518
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
12. #18011910C4semidirect
13. #18011909C4semidirect
19. C4×Dic298C4semidirect
22. C4×Q8×C149C4semidirect
92. C149#1518semidirect
107. C4×Q8#10597010semidirect

Maximal subgroups

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

subgroupindex
#237506442
#237505692
#237504792
#237504782
#237501792
#1518149