Finite Group Databasebeta

← #44549531

Subgroups — #44549531

Order 32128.

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

normal subgroups only

This group has 228 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
2#30632039C211yesmaximal, characteristic, complemented
3#30631983C211yesmaximal, characteristic, complemented
4#30631978C211yesmaximal, characteristic
5#30631417C211yesmaximal, characteristic, complemented
6#30631414C211yesmaximal, characteristic
7#332×C251C211yesmaximal, characteristic, complemented
8C2×Q8×D251—21no—
9#22548715C2211yescharacteristic
10#22548714—21no—
11#22548693—22no—
12#22548691—21no—
13C4×Dic502C2211yescharacteristic
14C4×D1004C2211yescharacteristic
15#22548677—21no—
16#22548649—21no—
17#22548647—21no—
18#22548640—21no—
19#22548638—22no—
20#22548637—21no—
21C4×C251⋊C8C2211yescharacteristic
22C4⋊Q8×C251C2211yescharacteristic
23C4⋊C8×C251C2211yescharacteristic
24C4⋊C8×C251C2211yescharacteristic
25C2×Dic502—22no—
26C2×Dic502—21no—
27C2×Dic502D411yescharacteristic
28Q8×D251—42no—
29Q8×D251—42no—
30C2×D1004D411yescharacteristic
31C2×C4×D251—22no—
32C2×C4×D251—21no—
33C2×C251⋊C8—21no—
34C4⋊Dic251—21no—
35C4⋊Dic251—21no—
36C4⋊Dic251D411yescharacteristic
37C4⋊Dic251D411yescharacteristic
38Dic251⋊C4—22no—
39Dic251⋊C4—21no—
40(C2×D251)⋊C4—22no—
41(C2×D251)⋊C4—21no—
42C4×Dic251—21no—
43C2×Q8×C251—21no—
44C2×C8×C251—21no—
45C2×C8×C251—21no—
46C4⋊C4×C251—21no—
47C4⋊C4×C251D412yes—
48C42×C251C2311yescharacteristic
49C22×D251—21no—
50Dic502—21no—
51Dic502—44no—
52Dic502—42no—
53Dic502SD1612yes—
54D1004—21no—
55D1004Q1612yes—
56C2×Dic251—21no—
57C2×Dic251—21no—
58C2×Dic251—21no—
59C2×Dic251—41no—
60C4×D251—44no—
61C4×D251—41no—
62C4×D251—41no—
63C251⋊C8—41no—
64Q8×C251—41no—
65Q8×C251—41no—
66C2×C4×C251—22no—
67C2×C4×C251C2×D411yescharacteristic
68C2×C4×C251C2×D411yescharacteristic
69C2×C4×C251C2×D411yescharacteristic
70C8×C251—41no—
71C8×C251—41no—
72C22×C251#12011yescharacteristic
73C2×D251—22no—
74C2×D251—41no—
75C2×D251—41no—
76C4×C251—21no—
77C4×C251—42no—
78C4×C251C2×SD1611yescharacteristic
79C4×C251C2×Q1611yescharacteristic
80C4×C251AGL(1,ℤ/8)11yescharacteristic
81C4×C251#13711yescharacteristic
82Dic251—22no—
83Dic251—41no—
84Dic251—41no—
85Dic251—81no—
86C2×C251#45011yescharacteristic
87C2×C251#45111yescharacteristic
88C2×C251#45411yescharacteristic
89D251—42no—
90C251#163711yescharacteristic, complemented, Sylow
91#1637—2511nomaximal, Sylow
92D4×Q8—2511no—
93#487—2511no—
94#477—2511no—
95#476—2511no—
96#332D25111yescharacteristic, complemented
97Q8⋊C8—2511no—
98D4⋊C8—2511no—
99C22×Q8—5021no—
100C4⋊Q8—5021no—
101C4⋊Q8—2511no—
102C4⋊Q8C2×D25111yescharacteristic
103C22⋊Q8—5021no—
104C22⋊Q8—5022no—
105C4×Q8—2511no—
106C4×D4—5021no—
107C4×D4—2511no—
108#107—5021no—
109#106—5021no—
110C4⋊C8C2×D25111yescharacteristic
111C4⋊C8C2×D25111yescharacteristic
112#103—5021no—
113#103—5022no—
114#102—5021no—
115C4×C8—2511no—
116C2×Q8—21no—
117C2×Q8—10042no—
118C2×Q8—10042no—
119C2×Q8—5022no—
120C2×Q8—5021no—
121C2×Q8—2511no—
122C2×D4—2511no—
123C22×C4—5022no—
124C22×C4—5021no—
125C2×C8—21no—
126C2×C8—21no—
127C2×C8—5021no—
128C4⋊C4—21no—
129C4⋊C4—5022no—
130C4⋊C4—5021no—
131C4⋊C4—5021no—
132C4⋊C4—5021no—
133C4⋊C4—2511no—
134C4⋊C4—2511no—
135C4⋊C4D100412yes—
136C22⋊C4—5022no—
137C22⋊C4—5021no—
138C42—5021no—
139C42C22×D25111yescharacteristic
140C23—5021no—
141Q8—41no—
142Q8—41no—
143Q8—10042no—
144Q8—10044no—
145Q8—5021no—
146Q8—2512no—
147D4—5021no—
148D4—2512no—
149C2×C4—22no—
150C2×C4—10044no—
151C2×C4—10041no—
152C2×C4—10041no—
153C2×C4—10041no—
154C2×C4—5021no—
155C2×C4—5021no—
156C2×C4—5021no—
157C2×C4D4×D25111yescharacteristic
158C2×C4D4×D25111yescharacteristic
159C2×C4C2×D100411yescharacteristic
160C8—41no—
161C8—41no—
162C8—10041no—
163C22—10041no—
164C22—10041no—
165C22—5022no—
166C22#2254868511yescharacteristic
167C4—21no—
168C4—42no—
169C4—20081no—
170C4—10041no—
171C4—10041no—
172C4—5022no—
173C4SD16×D25111yescharacteristic
174C4Q16×D25111yescharacteristic
175C4#2254873911yescharacteristic
176C4#2254874411yescharacteristic
177C2—10042no—
178C2#3063183911yescharacteristic
179C2#3063184411yescharacteristic
180C2#3063186211yescharacteristic
subgroupG/H
centerC22#22548685
commutator, cosocleC42×C251C23
FrattiniC42C22×D251
Fitting#332×C251C2
socleC22×C251#120
prime radicalC2×D1004D4
hypercenter#332D251
hypocenterC251#1637
LCSG ▷ C42×C251 ▷ C22×C251 ▷ C251
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #30632039C2semidirect
3. #30631983C2semidirect
5. #30631417C2semidirect
7. #332×C251C2semidirect
90. C251#1637semidirect
96. #332D251semidirect

Maximal subgroups

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

subgroupindex
#306323522
#306320392
#306319832
#306319782
#306314172
#306314142
#332×C2512
#1637251