Finite Group Databasebeta

← #34043400

Subgroups — #34043400

Order 19072.

198 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 65 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#23750180C211yesmaximal, characteristic
2#23749681C211yesmaximal, characteristic
3#23749677C211yesmaximal, characteristic
4#23749374C211yesmaximal, characteristic, complemented
5#23749372C211yesmaximal, characteristic, complemented
6#23749370C211yesmaximal, characteristic, complemented
7#333×C149C211yesmaximal, characteristic, complemented
8#18011911C2211yescharacteristic
9#18011902—21no—
10#18011891—21no—
11#18011887C412yes—
12Q8×Dic149C412yes—
13#18011876—21no—
14#18011869—21no—
15C42×D149C2211yescharacteristic
16C4⋊#11924746C2211yescharacteristic
17C4⋊#11924746C2211yescharacteristic
18#18011823—21no—
19#18011823—21no—
20#18011821—21no—
21C8×Dic149—21no—
22C4⋊Q8×C149C2211yescharacteristic
23C4⋊C8×C149C2211yescharacteristic
24C4⋊C8×C149C2211yescharacteristic
25C2×Dic298—21no—
26C2×C4×D149C2×C411yescharacteristic
27C2×C4×D149D411yescharacteristic
28C2×C4×D149D411yescharacteristic
29C2×#11924746—21no—
30C2×#11924746—21no—
31C4⋊Dic149—22no—
32C4⋊Dic149—21no—
33C4⋊Dic149C2×C412yes—
34#14558715—22no—
35#14558713—22no—
36C4×Dic149—22no—
37C4×Dic149C2×C411yescharacteristic
38C4×Dic149D411yescharacteristic
39C4×Dic149D411yescharacteristic
40C2×Q8×C149C2×C412yes—
41C2×C8×C149—21no—
42C2×C8×C149—21no—
43C4⋊C4×C149—21no—
44C4⋊C4×C149—21no—
45C42×C149C2311yescharacteristic
46C22×D149C22⋊C411yescharacteristic
47Dic298—41no—
48Dic298—41no—
49C2×Dic149—22no—
50C2×Dic149C22⋊C411yescharacteristic
51C2×Dic149C22⋊C411yescharacteristic
52C2×Dic149C22⋊C411yescharacteristic
53C4×D149—21no—
54C4×D149—21no—
55C4×D149—21no—
56C4×D149—21no—
57C4×D149—41no—
58#11924746—41no—
59#11924746—41no—
60Q8×C149—42no—
61C2×C4×C149—22no—
62C2×C4×C149C22×C411yescharacteristic
63C2×C4×C149C2×D411yescharacteristic
64C2×C4×C149C2×D411yescharacteristic
65C8×C149—41no—
66C8×C149—41no—
67C22×C149C2×C22⋊C411yescharacteristic
68C2×D149—21no—
69C2×D149—21no—
70C2×D149—21no—
71C4×C149—21no—
72C4×C149—42no—
73C4×C149#13511yescharacteristic
74C4×C149#13511yescharacteristic
75C4×C149#13711yescharacteristic
76C4×C149#13711yescharacteristic
77Dic149—21no—
78Dic149—21no—
79Dic149—21no—
80Dic149—42no—
81C2×C149#41311yescharacteristic
82C2×C149#41611yescharacteristic
83C2×C149#41911yescharacteristic
84D149—41no—
85C149#155411yescharacteristic, complemented, Sylow
86#1554—1491nomaximal, Sylow
87#533—1491no—
88#432—1491no—
89#431—1491no—
90#333—1491no—
91#333D14911yescharacteristic, complemented
92#332—1491no—
93#332—1491no—
94C4⋊Q8—1491no—
95C4⋊Q8C2×D14911yescharacteristic
96#125—2981no—
97C22⋊Q8—2981no—
98C22⋊Q8—1492no—
99C4×Q8—2981no—
100C4×Q8—1492no—
101#117—2981no—
102C2×C42—1491no—
103C4⋊C8—1491no—
104C4⋊C8—1491no—
105C4⋊C8C2×D14911yescharacteristic
106C4⋊C8C2×D14911yescharacteristic
107C22⋊C8—2981no—
108C22⋊C8—2981no—
109#97—2981no—
110C4×C8—2981no—
111C2×Q8—2981no—
112C2×Q8C4×D14912yes—
113C22×C4—1491no—
114C22×C4—1491no—
115C22×C4—1491no—
116C2×C8—21no—
117C2×C8—21no—
118C2×C8—2981no—
119C2×C8—2981no—
120C4⋊C4—21no—
121C4⋊C4—21no—
122C4⋊C4—2982no—
123C4⋊C4—2982no—
124C4⋊C4—2981no—
125C4⋊C4—1492no—
126C22⋊C4—2982no—
127C42—2982no—
128C42—1491no—
129C42—1491no—
130C42—1491no—
131C42C22×D14911yescharacteristic
132C23—1491no—
133Q8—42no—
134Q8—5961no—
135Q8—5961no—
136C2×C4—22no—
137C2×C4—2981no—
138C2×C4—2981no—
139C2×C4—2981no—
140C2×C4—2981no—
141C2×C4—2982no—
142C2×C4—5961no—
143C2×C4—1491no—
144C2×C4—1491no—
145C2×C4—1491no—
146C2×C4C2×C4×D14911yescharacteristic
147C2×C4D4×D14911yescharacteristic
148C2×C4D4×D14911yescharacteristic
149C8—41no—
150C8—41no—
151C8—5961no—
152C8—5961no—
153C22—2981no—
154C22—2981no—
155C22—2981no—
156C22C22⋊C4×D14911yescharacteristic
157C4—21no—
158C4—42no—
159C4—2981no—
160C4—2981no—
161C4—2981no—
162C4—5962no—
163C4#1801193211yescharacteristic
164C4#1801193411yescharacteristic
165C4#1801194011yescharacteristic
166C4#1801194311yescharacteristic
167C2—5961no—
168C2#2374960611yescharacteristic
169C2#2374962011yescharacteristic
170C2#2374963211yescharacteristic
subgroupG/H
centerC22C22⋊C4×D149
commutatorC2×C4×C149C22×C4
FrattiniC42C22×D149
Fitting#333×C149C2
socleC22×C149C2×C22⋊C4
prime radicalC22×D149C22⋊C4
cosocleC42×C149C23
hypercenter#333D149
hypocenterC149#1554
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
4. #23749374C2semidirect
5. #23749372C2semidirect
6. #23749370C2semidirect
7. #333×C149C2semidirect
85. C149#1554semidirect
91. #333D149semidirect

Maximal subgroups

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

subgroupindex
#237501802
#237496812
#237496772
#237493742
#237493722
#237493702
#333×C1492
#1554149