Finite Group Databasebeta

← #2027×C229 #44419088

Subgroups — #2027×C229 #44419088

Order 29312.

282 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 84 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×C229C211yesmaximal, characteristic, complemented
2#418×C229C212yesmaximal
3#390×C229C211yesmaximal, characteristic
4#343×C229C211yesmaximal, characteristic, complemented
5#339×C229C212yesmaximal, complemented
6C22×D4×C229C2211yescharacteristic
7C2×M16×C229C2212yes—
8C4⋊Q8×C229—22no—
9#125×C229—22no—
10C22⋊Q8×C229—22no—
11#117×C229C2212yes—
12C2×C4⋊C4×C229C2211yescharacteristic
13C2×C22⋊C4×C229—22no—
14C2×C42×C229C2211yescharacteristic
15#102×C229—22no—
16#102×C229—22no—
17C24×C229—21no—
18C2×Q8×C229—22no—
19C2×D4×C229—22no—
20C2×D4×C229—22no—
21C2×D4×C229—21no—
22C2×D4×C229Q812yescomplemented
23C22×C4×C229—21no—
24C22×C4×C229D412yes—
25C22×C4×C229C2311yescharacteristic
26M16×C229—22no—
27M16×C229—22no—
28C2×C8×C229—22no—
29C4⋊C4×C229—22no—
30C4⋊C4×C229—24no—
31C4⋊C4×C229—22no—
32C4⋊C4×C229D412yes—
33C4⋊C4×C229D412yes—
34C22⋊C4×C229—22no—
35C22⋊C4×C229—44no—
36C42×C229—22no—
37C42×C229—22no—
38C23×C229—22no—
39C23×C229—42no—
40C23×C229—42no—
41C23×C229—41no—
42C23×C229—41no—
43C23×C229C2×D411yescharacteristic
44Q8×C229—82no—
45D4×C229—24no—
46D4×C229—42no—
47C2×C4×C229—22no—
48C2×C4×C229—22no—
49C2×C4×C229—22no—
50C2×C4×C229—22no—
51C2×C4×C229—41no—
52C2×C4×C229—41no—
53C2×C4×C229—42no—
54C2×C4×C229C2×D412yes—
55C2×C4×C229C2×Q811yescharacteristic
56C2×C4×C229#4112yes—
57C2×C4×C229#4111yescharacteristic
58C8×C229—42no—
59C22×C229—21no—
60C22×C229—21no—
61C22×C229—44no—
62C22×C229—42no—
63C22×C229—82no—
64C22×C229—81no—
65C22×C229—81no—
66C22×C229#12011yescharacteristic
67C22×C229C22⋊Q811yescharacteristic
68C22×C229#12411yescharacteristic
69C4×C229—42no—
70C4×C229—42no—
71C4×C229—42no—
72C4×C229—42no—
73C4×C229C22⋊Q812yes—
74C4×C229#12412yes—
75C2×C229—21no—
76C2×C229—21no—
77C2×C229—82no—
78C2×C229#39311yescharacteristic
79C2×C229#45311yescharacteristic
80C2×C229#45411yescharacteristic
81C229#202711yescharacteristic, direct product factor, Sylow
82#2027C22911yesmaximal, characteristic, direct product factor, Sylow
83#544C2×C22911yescharacteristic, complemented
84#418C2×C22912yes—
85#390C2×C22911yescharacteristic
86#343C2×C22911yescharacteristic, complemented
87#339C2×C22912yescomplemented
88C22×D4C22×C22911yescharacteristic
89C2×M16C22×C22912yes—
90C4⋊Q8—22no—
91#125—22no—
92C22⋊Q8—22no—
93#117C22×C22912yes—
94C2×C4⋊C4C22×C22911yescharacteristic
95C2×C22⋊C4—22no—
96C2×C42C22×C22911yescharacteristic
97#102—22no—
98#102—22no—
99C24—21no—
100C2×Q8—22no—
101C2×D4—22no—
102C2×D4—22no—
103C2×D4—21no—
104C2×D4Q8×C22912yescomplemented
105C22×C4—21no—
106C22×C4D4×C22912yes—
107C22×C4C23×C22911yescharacteristic
108M16—22no—
109M16—22no—
110C2×C8—22no—
111C4⋊C4—22no—
112C4⋊C4—24no—
113C4⋊C4—22no—
114C4⋊C4D4×C22912yes—
115C4⋊C4D4×C22912yes—
116C22⋊C4—22no—
117C22⋊C4—44no—
118C42—22no—
119C42—22no—
120C23—22no—
121C23—42no—
122C23—42no—
123C23—41no—
124C23—41no—
125C23C2×D4×C22911yescharacteristic
126Q8—82no—
127D4—24no—
128D4—42no—
129C2×C4—22no—
130C2×C4—22no—
131C2×C4—22no—
132C2×C4—22no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—42no—
136C2×C4C2×D4×C22912yes—
137C2×C4C2×Q8×C22911yescharacteristic
138C2×C4#41×C22912yes—
139C2×C4#41×C22911yescharacteristic
140C8—42no—
141C22—21no—
142C22—21no—
143C22—44no—
144C22—42no—
145C22—82no—
146C22—81no—
147C22—81no—
148C22#120×C22911yescharacteristic
149C22C22⋊Q8×C22911yescharacteristic
150C22#124×C22911yescharacteristic
151C4—42no—
152C4—42no—
153C4—42no—
154C4—42no—
155C4C22⋊Q8×C22912yes—
156C4#124×C22912yes—
157C2—21no—
158C2—21no—
159C2—82no—
160C2#393×C22911yescharacteristic
161C2#453×C22911yescharacteristic
162C2#454×C22911yescharacteristic
subgroupG/H
center, socleC22×C229#120
commutator, Frattini, cosocleC22×C4C23×C229
prime radicalC22×D4×C229C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C229 ◁ C22×C4×C229 ◁ G

Complements

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

NH ≅ G/Ntype
1. #544×C229C2semidirect
4. #343×C229C2semidirect
5. #339×C229C2semidirect
22. C2×D4×C229Q8semidirect
81. C229#2027direct (N × H)
82. #2027C229direct (N × H)
83. #544C2×C229semidirect
86. #343C2×C229semidirect
87. #339C2×C229semidirect
104. C2×D4Q8×C229semidirect

Maximal subgroups

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

subgroupindex
#544×C2292
#418×C2292
#390×C2292
#343×C2292
#339×C2292
#2027229