Finite Group Databasebeta

← #44549678

Subgroups — #44549678

Order 32128.

196 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 45 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#30632441C211yesmaximal, characteristic
2#30632097C211yesmaximal, characteristic, complemented
3#30632096C211yesmaximal, characteristic, complemented
4#30632081C211yesmaximal, characteristic
5#30631428C211yesmaximal, characteristic, complemented
6#30631426C211yesmaximal, characteristic
7#330×C251C211yesmaximal, characteristic, complemented
8C2×Dic1004—21no—
9C2×#16860799—21no—
10#22548715C2211yescharacteristic
11#22548714—21no—
12#22548710—21no—
13#22548710—21no—
14#22548707C2211yescharacteristic
15#22548703C2211yescharacteristic
16#22548700—21no—
17#22548695—21no—
18#22548693—21no—
19#22548649—21no—
20#22548648—21no—
21#22548647—21no—
22#22548646—21no—
23#22548626C2211yescharacteristic
24#125×C251C2211yescharacteristic
25#97×C251C2211yescharacteristic
26#97×C251C2211yescharacteristic
27C2×Dic502—21no—
28C2×Dic502—21no—
29C2×Dic502D411yescharacteristic
30C2×D1004D411yescharacteristic
31C2×C4×D251—21no—
32Dic1004—42no—
33#16860799—42no—
34C2×C251⋊C8—21no—
35C4⋊Dic251—21no—
36C4⋊Dic251—21no—
37C4⋊Dic251—21no—
38C4⋊Dic251D411yescharacteristic
39C4⋊Dic251D411yescharacteristic
40Dic251⋊C4—21no—
41Dic251⋊C4—21no—
42Dic251⋊C4—21no—
43(C2×D251)⋊C4—21no—
44(C2×D251)⋊C4—21no—
45(C2×D251)⋊C4—21no—
46(C2×D251)⋊C4—21no—
47(C2×D251)⋊C4—21no—
48C4×Dic251—21no—
49C2×C8×C251—21no—
50C2×C8×C251—21no—
51C4⋊C4×C251—21no—
52C4⋊C4×C251—21no—
53C4⋊C4×C251D411yescharacteristic
54C4⋊C4×C251D411yescharacteristic
55C42×C251C2311yescharacteristic
56C22×D251—21no—
57Dic502—41no—
58Dic502—41no—
59Dic502—41no—
60Dic502—81no—
61D1004—41no—
62C2×Dic251—21no—
63C2×Dic251—21no—
64C2×Dic251—21no—
65C2×Dic251—41no—
66C4×D251—81no—
67C251⋊C8—22no—
68C2×C4×C251—21no—
69C2×C4×C251—21no—
70C2×C4×C251C2×D411yescharacteristic
71C2×C4×C251C2×D411yescharacteristic
72C2×C4×C251C2×D411yescharacteristic
73C8×C251—22no—
74C8×C251—22no—
75C22×C251#12011yescharacteristic
76C2×D251—41no—
77C2×D251—41no—
78C2×D251—41no—
79C4×C251—21no—
80C4×C251—21no—
81C4×C251—21no—
82C4×C251—41no—
83C4×C251—41no—
84Dic251—41no—
85Dic251—41no—
86Dic251—41no—
87Dic251—81no—
88C2×C251#45311yescharacteristic
89C2×C251#45611yescharacteristic
90C2×C251#45611yescharacteristic
91D251—81no—
92C251#166011yescharacteristic, complemented, Sylow
93#1660—2511nomaximal, Sylow
94#563—2511no—
95#501—2511no—
96#501—2511no—
97#497—2511no—
98#330—2511no—
99#330D25111yescharacteristic, complemented
100#329—2511no—
101C2×Q16—5021no—
102C2×SD16—5021no—
103C4⋊Q8—5021no—
104C4⋊Q8—2511no—
105#126—5021no—
106#126—5021no—
107#125—2511no—
108#125C2×D25111yescharacteristic
109#124—2511no—
110#123—5021no—
111C22⋊Q8—5021no—
112C22⋊Q8—5021no—
113#107—5021no—
114#107—5021no—
115#106—5021no—
116#106—5021no—
117#97—2511no—
118#97C2×D25111yescharacteristic
119#97C2×D25111yescharacteristic
120C2×Q8—5021no—
121C2×Q8—5021no—
122C2×Q8—2511no—
123C2×D4—2511no—
124C22×C4—5021no—
125Q16—10042no—
126SD16—10042no—
127C2×C8—21no—
128C2×C8—21no—
129C2×C8—5021no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—5021no—
133C4⋊C4—5021no—
134C4⋊C4—5021no—
135C4⋊C4—5021no—
136C4⋊C4—5021no—
137C4⋊C4—5021no—
138C4⋊C4—2511no—
139C4⋊C4—2511no—
140C4⋊C4D100411yescharacteristic
141C4⋊C4D100411yescharacteristic
142C22⋊C4—5021no—
143C22⋊C4—5021no—
144C22⋊C4—5021no—
145C22⋊C4—5021no—
146C22⋊C4—5021no—
147C42—5021no—
148C42C22×D25111yescharacteristic
149C23—5021no—
150Q8—20081no—
151Q8—10041no—
152Q8—10041no—
153Q8—10041no—
154D4—10041no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—20081no—
158C2×C4—10041no—
159C2×C4—5021no—
160C2×C4—5021no—
161C2×C4—5021no—
162C2×C4D4×D25111yescharacteristic
163C2×C4D4×D25111yescharacteristic
164C2×C4C2×D100411yescharacteristic
165C8—22no—
166C8—22no—
167C8—5022no—
168C22—10041no—
169C22—10041no—
170C22—10041no—
171C22#2254868511yescharacteristic
172C4—21no—
173C4—21no—
174C4—21no—
175C4—41no—
176C4—41no—
177C4—20081no—
178C4—10041no—
179C4—10041no—
180C4—10041no—
181C2—20081no—
182C2#3063185611yescharacteristic
183C2#3063187111yescharacteristic
184C2#3063187211yescharacteristic
subgroupG/H
centerC22#22548685
commutator, cosocleC42×C251C23
FrattiniC42C22×D251
Fitting#330×C251C2
socleC22×C251#120
prime radicalC2×D1004D4
hypercenter#330D251
hypocenterC251#1660
LCSG ▷ C42×C251 ▷ C22×C251 ▷ C251
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #30632097C2semidirect
3. #30632096C2semidirect
5. #30631428C2semidirect
7. #330×C251C2semidirect
92. C251#1660semidirect
99. #330D251semidirect

Maximal subgroups

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

subgroupindex
#306324412
#306320972
#306320962
#306320812
#306314282
#306314262
#330×C2512
#1660251