Finite Group Databasebeta

← #34071141

Subgroups — #34071141

Order 19328.

224 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 41 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#23752942C211yesmaximal, characteristic, complemented
2#23752397C212yesmaximal
3#23752394C211yesmaximal, characteristic
4#23752010C212yesmaximal, complemented
5#356×C151C211yesmaximal, characteristic, complemented
6#18012787C2211yescharacteristic
7#18012772—22no—
8#18012770—21no—
9#18012738—22no—
10#18012737—21no—
11#18012737C2212yes—
12C4×Dic302—21no—
13#18012704—22no—
14#18012667—21no—
15#18012665—22no—
16#18012658C2211yescharacteristic
17C4⋊Q8×C151C2211yescharacteristic
18#101×C151C2212yes—
19#14559005—41no—
20#14559004—21no—
21#14559004—22no—
22C2×Dic302—21no—
23C2×Dic302—21no—
24C2×Dic302D412yes—
25Q8×D151—41no—
26Dic604—42no—
27#14558994—41no—
28#14558993—42no—
29#14558991—41no—
30#14558988—21no—
31C4⋊Dic151—21no—
32Dic151⋊C4—22no—
33Dic151⋊C4—22no—
34Dic151⋊C4—22no—
35C4×Dic151—21no—
36C4×Dic151—22no—
37C4×Dic151D412yes—
38C2×Q8×C151D411yescharacteristic
39C2×Q8×C151C2311yescharacteristic
40M16×C151—22no—
41C4⋊C4×C151—22no—
42C42×C151D411yescharacteristic
43Dic302—24no—
44Dic302—21no—
45Dic302—22no—
46Dic302—42no—
47Dic302—81no—
48D604—21no—
49D604—22no—
50C22⋊D151—41no—
51C2×Dic151—22no—
52C2×Dic151—22no—
53C4×D151—42no—
54C4×D151—41no—
55C151⋊C8—41no—
56Q8×C151—41no—
57Q8×C151—41no—
58C2×C4×C151—21no—
59C2×C4×C151—21no—
60C2×C4×C151C2×D412yes—
61C2×C4×C151C2×D411yescharacteristic
62C8×C151—42no—
63C22×C151#12011yescharacteristic
64C2×D151—41no—
65C4×C151—22no—
66C4×C151—22no—
67C4×C151—21no—
68C4×C151—41no—
69Dic151—24no—
70Dic151—41no—
71Dic151—42no—
72C2×C151—21no—
73C2×C151B(4,𝔽2)11yescharacteristic
74D151—81no—
75C151#220511yescharacteristic, complemented, Sylow
76#2205—1511nomaximal, Sylow
77Q82—1511no—
78#456—1511no—
79#456—1512no—
80#356—1512no—
81#356D15111yescharacteristic, complemented
822−1+4—1511no—
83#137—3022no—
84#137—3021no—
85C4⋊Q8—3022no—
86C4⋊Q8—3021no—
87C4⋊Q8—1512no—
88C4⋊Q8C2×D15111yescharacteristic
89C4×Q8—3022no—
90C4×Q8—3021no—
91#104—3022no—
92#104—3021no—
93#101—1511no—
94#101C2×D15112yes—
95#41—3022no—
96#41—3021no—
97#41—6041no—
98C2×Q8—3021no—
99C2×Q8—3021no—
100C2×Q8—6041no—
101C2×Q8—1512no—
102C2×Q8D60411yescharacteristic
103C2×Q8C22×D15111yescharacteristic
104Q16—6042no—
105Q16—6041no—
106SD16—6042no—
107SD16—6041no—
108M16—22no—
109M16—3021no—
110C4⋊C4—22no—
111C4⋊C4—3022no—
112C4⋊C4—3021no—
113C4⋊C4—3022no—
114C4⋊C4—3022no—
115C42—3022no—
116C42—3021no—
117C42—1512no—
118C42D60411yescharacteristic
119Q8—41no—
120Q8—41no—
121Q8—3024no—
122Q8—3022no—
123Q8—3021no—
124Q8—6042no—
125Q8—12081no—
126D4—3022no—
127D4—3021no—
128D4—6041no—
129C2×C4—21no—
130C2×C4—21no—
131C2×C4—3022no—
132C2×C4—3022no—
133C2×C4—6042no—
134C2×C4—6041no—
135C2×C4D4×D15112yes—
136C2×C4C2×D60411yescharacteristic
137C8—42no—
138C8—6041no—
139C22—6041no—
140C22#1801270911yescharacteristic
141C4—22no—
142C4—22no—
143C4—21no—
144C4—41no—
145C4—3024no—
146C4—6042no—
147C4—6041no—
148C2—21no—
149C2—12081no—
150C2#2375240011yescharacteristic
subgroupG/H
centerC2#23752400
commutator, cosocleC2×Q8×C151C23
FrattiniC2×Q8C22×D151
Fitting#356×C151C2
socleC2×C151B(4,𝔽2)
prime radical#18012787C22
hypercenter#356D151
hypocenterC151#2205
LCSG ▷ C2×Q8×C151 ▷ C22×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #356

Complements

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

NH ≅ G/Ntype
1. #23752942C2semidirect
4. #23752010C2semidirect
5. #356×C151C2semidirect
75. C151#2205semidirect
81. #356D151semidirect

Maximal subgroups

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

subgroupindex
#237529422
#237523972
#237523942
#237520102
#356×C1512
#2205151