Finite Group Databasebeta

← #49120372

Subgroups — #49120372

Order 36224.

216 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 53 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#31827189C211yesmaximal, characteristic, complemented
2#31826813C211yesmaximal, characteristic, complemented
3#31826666C211yesmaximal, characteristic, complemented
4#31826661C211yesmaximal, characteristic
5#31826195C211yesmaximal, characteristic, complemented
6#31826192C211yesmaximal, characteristic, complemented
7#332×C283C211yesmaximal, characteristic, complemented
8C2×#17985381—21no—
9C2×D2264—21no—
10#22583607C2211yescharacteristic
11#22583605—22no—
12#22583599—21no—
13#22583590—21no—
14Q8×Dic283—21no—
15C4×Dic566C2211yescharacteristic
16C4×D1132C2211yescharacteristic
17#22583568—21no—
18#22583532—21no—
19#22583532—21no—
20#22583530—22no—
21C4×C283⋊C8C2211yescharacteristic
22C4⋊Q8×C283C2211yescharacteristic
23C4⋊C8×C283C2211yescharacteristic
24C4⋊C8×C283C2211yescharacteristic
25C2×Dic566D411yescharacteristic
26C2×D1132—21no—
27C2×D1132—21no—
28C2×D1132—21no—
29C2×D1132D411yescharacteristic
30C2×C4×D283—21no—
31#17985381—42no—
32D2264—42no—
33C2×C283⋊C8—21no—
34C4⋊Dic283—22no—
35C4⋊Dic283D411yescharacteristic
36C4⋊Dic283D411yescharacteristic
37Dic283⋊C4—21no—
38(C2×D283)⋊C4—22no—
39(C2×D283)⋊C4—22no—
40(C2×D283)⋊C4—21no—
41C4×Dic283—22no—
42C4×Dic283—21no—
43C2×Q8×C283—21no—
44C2×C8×C283—21no—
45C2×C8×C283—21no—
46C4⋊C4×C283—21no—
47C4⋊C4×C283D412yes—
48C42×C283C2311yescharacteristic
49C22×D283—21no—
50C22×D283—41no—
51Dic566—21no—
52Dic566—21no—
53D1132—21no—
54D1132—21no—
55D1132—42no—
56D1132—41no—
57D1132—41no—
58D1132—41no—
59D1132—41no—
60C2×Dic283—21no—
61C2×Dic283—21no—
62C2×Dic283—21no—
63C4×D283—41no—
64C4×D283—41no—
65C283⋊C8—41no—
66Q8×C283—41no—
67Q8×C283—41no—
68C2×C4×C283—22no—
69C2×C4×C283C2×D411yescharacteristic
70C2×C4×C283C2×D411yescharacteristic
71C2×C4×C283C2×D411yescharacteristic
72C8×C283—41no—
73C8×C283—41no—
74C22×C283#12011yescharacteristic
75C2×D283—41no—
76C2×D283—41no—
77C2×D283—41no—
78C2×D283—81no—
79C2×D283—81no—
80C2×D283—81no—
81C4×C283—21no—
82C4×C283—42no—
83C4×C283#13511yescharacteristic
84C4×C283#13511yescharacteristic
85C4×C283AGL(1,ℤ/8)11yescharacteristic
86C4×C283AGL(1,ℤ/8)11yescharacteristic
87Dic283—41no—
88Dic283—41no—
89Dic283—41no—
90C2×C283#44911yescharacteristic
91C2×C283#44911yescharacteristic
92C2×C283#45411yescharacteristic
93D283—81no—
94D283—161no—
95C283#162811yescharacteristic, complemented, Sylow
96#1628—2831nomaximal, Sylow
97#556—2831no—
98#486—2831no—
99#460—2831no—
100#459—2831no—
101#332D28311yescharacteristic, complemented
102Q8⋊C8—2831no—
103D4⋊C8—2831no—
104C2×SD16—5661no—
105C2×D8—5661no—
106C4⋊Q8C2×D28311yescharacteristic
107#127—2831no—
108#126—5662no—
109#124—5661no—
110C22⋊Q8—5661no—
111C4×Q8—2831no—
112C4×Q8—5661no—
113C4×D4—2831no—
114#117—5661no—
115C4⋊C8C2×D28311yescharacteristic
116C4⋊C8C2×D28311yescharacteristic
117#102—5661no—
118#102—5661no—
119#102—5662no—
120C4×C8—2831no—
121C2×Q8—21no—
122C2×Q8—2831no—
123C2×D4—2831no—
124C2×D4—5661no—
125C2×D4—5661no—
126C2×D4—5661no—
127C22×C4—5661no—
128SD16—11322no—
129D8—11322no—
130C2×C8—21no—
131C2×C8—21no—
132C2×C8—5661no—
133C4⋊C4—21no—
134C4⋊C4—2831no—
135C4⋊C4—2831no—
136C4⋊C4—5662no—
137C4⋊C4—5661no—
138C4⋊C4D113212yes—
139C22⋊C4—5662no—
140C22⋊C4—5662no—
141C22⋊C4—5661no—
142C42—5662no—
143C42—5661no—
144C42C22×D28311yescharacteristic
145C23—5661no—
146C23—11321no—
147Q8—41no—
148Q8—41no—
149Q8—5661no—
150Q8—5661no—
151D4—5661no—
152D4—5661no—
153D4—11322no—
154D4—11321no—
155D4—11321no—
156D4—11321no—
157D4—11321no—
158C2×C4—22no—
159C2×C4—5661no—
160C2×C4—5661no—
161C2×C4—5661no—
162C2×C4—11321no—
163C2×C4—11321no—
164C2×C4D4×D28311yescharacteristic
165C2×C4D4×D28311yescharacteristic
166C2×C4C2×D113211yescharacteristic
167C8—41no—
168C8—41no—
169C8—11321no—
170C22—11321no—
171C22—11321no—
172C22—11321no—
173C22—22641no—
174C22—22641no—
175C22—22641no—
176C22#2258358011yescharacteristic
177C4—21no—
178C4—42no—
179C4—11321no—
180C4—11321no—
181C4—11321no—
182C4#2258363111yescharacteristic
183C4#2258363311yescharacteristic
184C4#2258363411yescharacteristic
185C4#2258363711yescharacteristic
186C2—45281no—
187C2—22641no—
188C2#3182661111yescharacteristic
189C2#3182661311yescharacteristic
190C2#3182664011yescharacteristic
subgroupG/H
centerC22#22583580
commutator, cosocleC42×C283C23
FrattiniC42C22×D283
Fitting#332×C283C2
socleC22×C283#120
prime radical#31826661C2
hypercenter#332D283
hypocenterC283#1628
LCSG ▷ C42×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
1. #31827189C2semidirect
2. #31826813C2semidirect
3. #31826666C2semidirect
5. #31826195C2semidirect
6. #31826192C2semidirect
7. #332×C283C2semidirect
95. C283#1628semidirect
101. #332D283semidirect

Maximal subgroups

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

subgroupindex
#318271892
#318268132
#318266662
#318266612
#318261952
#318261922
#332×C2832
#1628283