Finite Group Databasebeta

← #1611×C233 #44447643

Subgroups — #1611×C233 #44447643

Order 29824.

210 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 68 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#544×C233C211yesmaximal, characteristic
2#483×C233C212yesmaximal
3#398×C233C211yesmaximal, characteristic
4#328×C233C212yesmaximal
5#324×C233C211yesmaximal, characteristic
6C4⋊Q8×C233—22no—
7#125×C233—22no—
8C22⋊Q8×C233—21no—
9C22⋊Q8×C233C2212yes—
10#117×C233—21no—
11C2×C4⋊C4×C233—21no—
12C2×C4⋊C4×C233C2211yescharacteristic
13C2×C4⋊C4×C233C2211yescharacteristic
14#106×C233—22no—
15#103×C233—22no—
16C22⋊C8×C233C2212yes—
17#95×C233—21no—
18#95×C233C2211yescharacteristic
19C2×Q8×C233—21no—
20C2×Q8×C233D412yes—
21C22×C4×C233—21no—
22C22×C4×C233—21no—
23C22×C4×C233D411yescharacteristic
24C22×C4×C233D411yescharacteristic
25C22×C4×C233C2311yescharacteristic
26C2×C8×C233—22no—
27C4⋊C4×C233—21no—
28C4⋊C4×C233—21no—
29C4⋊C4×C233—21no—
30C4⋊C4×C233—22no—
31C4⋊C4×C233—22no—
32C4⋊C4×C233—22no—
33C4⋊C4×C233—22no—
34C4⋊C4×C233—42no—
35C4⋊C4×C233D412yes—
36C22⋊C4×C233—22no—
37C42×C233—22no—
38C23×C233C2×D411yescharacteristic
39Q8×C233—42no—
40Q8×C233—81no—
41C2×C4×C233—21no—
42C2×C4×C233—21no—
43C2×C4×C233—22no—
44C2×C4×C233—22no—
45C2×C4×C233—22no—
46C2×C4×C233—21no—
47C2×C4×C233—41no—
48C2×C4×C233—41no—
49C2×C4×C233—41no—
50C2×C4×C233—41no—
51C2×C4×C233—41no—
52C2×C4×C233—41no—
53C2×C4×C233—41no—
54C2×C4×C233SD1612yes—
55C2×C4×C233C2×D412yes—
56C8×C233—42no—
57C22×C233—21no—
58C22×C233—21no—
59C22×C233#12011yescharacteristic
60C22×C233C2×SD1611yescharacteristic
61C22×C233#13711yescharacteristic
62C4×C233—22no—
63C4×C233—22no—
64C4×C233—42no—
65C4×C233—42no—
66C4×C233—41no—
67C4×C233—42no—
68C4×C233—81no—
69C2×C233—21no—
70C2×C233—21no—
71C2×C233#44811yescharacteristic
72C2×C233#45611yescharacteristic
73C2×C233#45811yescharacteristic
74C233#161111yescharacteristic, direct product factor, Sylow
75#1611C23311yesmaximal, characteristic, direct product factor, Sylow
76#544C2×C23311yescharacteristic
77#483C2×C23312yes—
78#398C2×C23311yescharacteristic
79#328C2×C23312yes—
80#324C2×C23311yescharacteristic
81C4⋊Q8—22no—
82#125—22no—
83C22⋊Q8—21no—
84C22⋊Q8C22×C23312yes—
85#117—21no—
86C2×C4⋊C4—21no—
87C2×C4⋊C4C22×C23311yescharacteristic
88C2×C4⋊C4C22×C23311yescharacteristic
89#106—22no—
90#103—22no—
91C22⋊C8C22×C23312yes—
92#95—21no—
93#95C22×C23311yescharacteristic
94C2×Q8—21no—
95C2×Q8D4×C23312yes—
96C22×C4—21no—
97C22×C4—21no—
98C22×C4D4×C23311yescharacteristic
99C22×C4D4×C23311yescharacteristic
100C22×C4C23×C23311yescharacteristic
101C2×C8—22no—
102C4⋊C4—21no—
103C4⋊C4—21no—
104C4⋊C4—21no—
105C4⋊C4—22no—
106C4⋊C4—22no—
107C4⋊C4—22no—
108C4⋊C4—22no—
109C4⋊C4—42no—
110C4⋊C4D4×C23312yes—
111C22⋊C4—22no—
112C42—22no—
113C23C2×D4×C23311yescharacteristic
114Q8—42no—
115Q8—81no—
116C2×C4—21no—
117C2×C4—21no—
118C2×C4—22no—
119C2×C4—22no—
120C2×C4—22no—
121C2×C4—21no—
122C2×C4—41no—
123C2×C4—41no—
124C2×C4—41no—
125C2×C4—41no—
126C2×C4—41no—
127C2×C4—41no—
128C2×C4—41no—
129C2×C4SD16×C23312yes—
130C2×C4C2×D4×C23312yes—
131C8—42no—
132C22—21no—
133C22—21no—
134C22#120×C23311yescharacteristic
135C22C2×SD16×C23311yescharacteristic
136C22#137×C23311yescharacteristic
137C4—22no—
138C4—22no—
139C4—42no—
140C4—42no—
141C4—41no—
142C4—42no—
143C4—81no—
144C2—21no—
145C2—21no—
146C2#448×C23311yescharacteristic
147C2#456×C23311yescharacteristic
148C2#458×C23311yescharacteristic
subgroupG/H
center, socleC22×C233#120
commutator, Frattini, cosocleC22×C4C23×C233
prime radicalC23×C233C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C233 ◁ C22×C4×C233 ◁ G

Complements

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

NH ≅ G/Ntype
74. C233#1611direct (N × H)
75. #1611C233direct (N × H)

Maximal subgroups

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

subgroupindex
#544×C2332
#483×C2332
#398×C2332
#328×C2332
#324×C2332
#1611233