Finite Group Databasebeta

← #44549469

Subgroups — #44549469

Order 32128.

250 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 57 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#30632352C211yesmaximal, characteristic, complemented
2#30632035C211yesmaximal, characteristic, complemented
3#30631888C211yesmaximal, characteristic, complemented
4#30631883C211yesmaximal, characteristic
5#30631417C211yesmaximal, characteristic, complemented
6#30631414C211yesmaximal, characteristic, complemented
7#332×C251C211yesmaximal, characteristic, complemented
8C2×Q8×D251—21no—
9C2×#16860799—21no—
10C2×D2008—21no—
11#22548714—21no—
12#22548712C2211yescharacteristic
13#22548693—22no—
14#22548691—21no—
15C4×Dic502C2211yescharacteristic
16C4×D1004C2211yescharacteristic
17#22548677—21no—
18#22548637—21no—
19#22548637—21no—
20#22548635—22no—
21C4×C251⋊C8C2211yescharacteristic
22C4⋊Q8×C251C2211yescharacteristic
23C4⋊C8×C251C2211yescharacteristic
24C4⋊C8×C251C2211yescharacteristic
25C2×Dic502—22no—
26C2×Dic502D411yescharacteristic
27Q8×D251—42no—
28Q8×D251—42no—
29C2×D1004—21no—
30C2×D1004—21no—
31C2×D1004—21no—
32C2×D1004D411yescharacteristic
33C2×C4×D251—22no—
34C2×C4×D251—21no—
35#16860799—42no—
36D2008—42no—
37C2×C251⋊C8—21no—
38C4⋊Dic251D411yescharacteristic
39C4⋊Dic251D411yescharacteristic
40Dic251⋊C4—22no—
41Dic251⋊C4—21no—
42(C2×D251)⋊C4—22no—
43(C2×D251)⋊C4—21no—
44C4×Dic251—21no—
45C2×Q8×C251—21no—
46C2×C8×C251—21no—
47C2×C8×C251—21no—
48C4⋊C4×C251—21no—
49C4⋊C4×C251D412yes—
50C42×C251C2311yescharacteristic
51C22×D251—21no—
52C22×D251—41no—
53Dic502—21no—
54Dic502—44no—
55Dic502D812yescomplemented
56D1004—21no—
57D1004—42no—
58D1004—41no—
59D1004—41no—
60D1004—41no—
61D1004—41no—
62D1004SD1612yescomplemented
63C2×Dic251—21no—
64C2×Dic251—21no—
65C2×Dic251—21no—
66C4×D251—44no—
67C4×D251—41no—
68C4×D251—41no—
69C251⋊C8—41no—
70Q8×C251—41no—
71Q8×C251—41no—
72C2×C4×C251—22no—
73C2×C4×C251C2×D411yescharacteristic
74C2×C4×C251C2×D411yescharacteristic
75C2×C4×C251C2×D411yescharacteristic
76C8×C251—41no—
77C8×C251—41no—
78C22×C251#12011yescharacteristic
79C2×D251—22no—
80C2×D251—41no—
81C2×D251—41no—
82C2×D251—81no—
83C2×D251—81no—
84C2×D251—81no—
85C4×C251—21no—
86C4×C251—42no—
87C4×C251C2×D811yescharacteristic
88C4×C251C2×SD1611yescharacteristic
89C4×C251AGL(1,ℤ/8)11yescharacteristic
90C4×C251#13711yescharacteristic
91Dic251—22no—
92Dic251—41no—
93Dic251—41no—
94C2×C251#44711yescharacteristic
95C2×C251#44811yescharacteristic
96C2×C251#45411yescharacteristic
97D251—42no—
98D251—161no—
99C251#162711yescharacteristic, complemented, Sylow
100#1627—2511nomaximal, Sylow
101D4×Q8—2511no—
102#486—2511no—
103#460—2511no—
104#459—2511no—
105#332D25111yescharacteristic, complemented
106Q8⋊C8—2511no—
107D4⋊C8—2511no—
108C22×Q8—5021no—
109C2×SD16—5021no—
110C2×D8—5021no—
111C4⋊Q8—5021no—
112C4⋊Q8C2×D25111yescharacteristic
113#127—2511no—
114C22⋊Q8—5021no—
115C22⋊Q8—5022no—
116C4×Q8—2511no—
117C4×D4—5021no—
118C4×D4—2511no—
119C4⋊C8C2×D25111yescharacteristic
120C4⋊C8C2×D25111yescharacteristic
121#102—5021no—
122#102—5021no—
123#102—5022no—
124C4×C8—2511no—
125C2×Q8—21no—
126C2×Q8—10042no—
127C2×Q8—10042no—
128C2×Q8—5022no—
129C2×Q8—2511no—
130C2×D4—5021no—
131C2×D4—5021no—
132C2×D4—5021no—
133C2×D4—2511no—
134C22×C4—5022no—
135C22×C4—5021no—
136SD16—10042no—
137D8—10042no—
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—5021no—
141C4⋊C4—21no—
142C4⋊C4—5022no—
143C4⋊C4—5021no—
144C4⋊C4—2511no—
145C4⋊C4—2511no—
146C4⋊C4D100412yes—
147C22⋊C4—5022no—
148C22⋊C4—5021no—
149C42—5021no—
150C42C22×D25111yescharacteristic
151C23—10041no—
152C23—5021no—
153Q8—41no—
154Q8—41no—
155Q8—10044no—
156Q8—5021no—
157Q8—2512no—
158D4—10042no—
159D4—10041no—
160D4—10041no—
161D4—10041no—
162D4—10041no—
163D4—5021no—
164D4—2512no—
165C2×C4—22no—
166C2×C4—10044no—
167C2×C4—10041no—
168C2×C4—10041no—
169C2×C4—5021no—
170C2×C4—5021no—
171C2×C4—5021no—
172C2×C4D4×D25111yescharacteristic
173C2×C4D4×D25111yescharacteristic
174C2×C4C2×D100411yescharacteristic
175C8—41no—
176C8—41no—
177C8—10041no—
178C22—20081no—
179C22—20081no—
180C22—20081no—
181C22—10041no—
182C22—10041no—
183C22—5022no—
184C22#2254868511yescharacteristic
185C4—21no—
186C4—42no—
187C4—10041no—
188C4—10041no—
189C4—5022no—
190C4D8×D25111yescharacteristic
191C4SD16×D25111yescharacteristic
192C4#2254874211yescharacteristic
193C4#2254874711yescharacteristic
194C2—40161no—
195C2—10042no—
196C2#3063182211yescharacteristic
197C2#3063182711yescharacteristic
198C2#3063186211yescharacteristic
subgroupG/H
centerC22#22548685
commutator, cosocleC42×C251C23
FrattiniC42C22×D251
Fitting#332×C251C2
socleC22×C251#120
prime radical#30631883C2
hypercenter#332D251
hypocenterC251#1627
LCSG ▷ C42×C251 ▷ C22×C251 ▷ C251
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
1. #30632352C2semidirect
2. #30632035C2semidirect
3. #30631888C2semidirect
5. #30631417C2semidirect
6. #30631414C2semidirect
7. #332×C251C2semidirect
55. Dic502D8semidirect
62. D1004SD16semidirect
99. C251#1627semidirect
105. #332D251semidirect

Maximal subgroups

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

subgroupindex
#306323522
#306320352
#306318882
#306318832
#306314172
#306314142
#332×C2512
#1627251