Finite Group Databasebeta

← #44549535

Subgroups — #44549535

Order 32128.

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

normal subgroups only

This group has 194 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#30632407C211yesmaximal, characteristic
2#30632037C211yesmaximal, characteristic, complemented
3#30631979C211yesmaximal, characteristic, complemented
4#30631434C211yesmaximal, characteristic, complemented
5#30631417C211yesmaximal, characteristic, complemented
6D4⋊(C251⋊C8)C211yesmaximal, characteristic
7#476×C251C211yesmaximal, characteristic
8#22548715C2211yescharacteristic
9#22548708—22no—
10#22548702—21no—
11#22548694—21no—
12C4×Dic502C2211yescharacteristic
13#22548680—21no—
14#22548674—21no—
15#22548648—21no—
16C4⋊(C251⋊C8)C2211yescharacteristic
17#22548639—22no—
18#22548638—21no—
19C4×C251⋊C8C2211yescharacteristic
20C4⋊Q8×C251C2211yescharacteristic
21C4×D4×C251C2211yescharacteristic
22#106×C251—21no—
23C4⋊C8×C251C2211yescharacteristic
24#102×C251—21no—
25C2×Dic502—21no—
26C2×Dic502D411yescharacteristic
27C2×C251⋊C8—21no—
28C2×C251⋊C8—21no—
29C4⋊Dic251—21no—
30C4⋊Dic251D412yes—
31C4⋊Dic251D411yescharacteristic
32Dic251⋊C4—22no—
33Dic251⋊C4—21no—
34C22⋊Dic251—22no—
35C22⋊Dic251—22no—
36C4×Dic251—22no—
37C4×Dic251—21no—
38C2×Q8×C251—21no—
39C2×D4×C251D411yescharacteristic
40C22×C4×C251—21no—
41C2×C8×C251—21no—
42C4⋊C4×C251—21no—
43C4⋊C4×C251—21no—
44C4⋊C4×C251D411yescharacteristic
45C22⋊C4×C251—21no—
46C42×C251C2311yescharacteristic
47Dic502—21no—
48Dic502—21no—
49Dic502—41no—
50Dic502—41no—
51C2×Dic251—21no—
52C2×Dic251—21no—
53C2×Dic251—22no—
54C251⋊C8—41no—
55C251⋊C8—41no—
56C23×C251—21no—
57Q8×C251—42no—
58D4×C251—21no—
59D4×C251—21no—
60C2×C4×C251—21no—
61C2×C4×C251—41no—
62C2×C4×C251—41no—
63C2×C4×C251—41no—
64C2×C4×C251C2×D411yescharacteristic
65C2×C4×C251C2×D411yescharacteristic
66C2×C4×C251C2×D411yescharacteristic
67C8×C251—41no—
68C22×C251—41no—
69C22×C251—41no—
70C22×C251—41no—
71C22×C251#12011yescharacteristic
72C4×C251—21no—
73C4×C251—41no—
74C4×C251—81no—
75C4×C251#13511yescharacteristic
76C4×C251#13511yescharacteristic
77C4×C251#13711yescharacteristic
78C4×C251#13711yescharacteristic
79Dic251—41no—
80Dic251—42no—
81Dic251—41no—
82C2×C251—81no—
83C2×C251#45211yescharacteristic
84C2×C251#45211yescharacteristic
85C2×C251#45411yescharacteristic
86C251#163811yescharacteristic, complemented, Sylow
87#1638—2511nomaximal, Sylow
88#556—2511no—
89#487—2511no—
90#477—2511no—
91#476D25111yescharacteristic
92#332—2511no—
93Q8⋊C8—2511no—
94D4⋊C8—2511no—
95C4⋊Q8—2511no—
96C4⋊Q8C2×D25111yescharacteristic
97#126—5022no—
98#124—5021no—
99C22⋊Q8—5021no—
100C4×Q8—5021no—
101C4×Q8—2511no—
102C4×D4C2×D25111yescharacteristic
103#117—5021no—
104#107—5021no—
105#106—21no—
106C4⋊C8—2511no—
107C4⋊C8C2×D25111yescharacteristic
108#103—5021no—
109#103—5022no—
110#102—21no—
111C4×C8—2511no—
112C2×Q8—21no—
113C2×Q8—5021no—
114C2×Q8—2511no—
115C2×D4C22⋊D25111yescharacteristic
116C22×C4—21no—
117C2×C8—21no—
118C2×C8—5021no—
119C2×C8—5021no—
120C4⋊C4—21no—
121C4⋊C4—21no—
122C4⋊C4—5022no—
123C4⋊C4—5021no—
124C4⋊C4—5021no—
125C4⋊C4—2512no—
126C4⋊C4—2511no—
127C4⋊C4C22⋊D25111yescharacteristic
128C22⋊C4—21no—
129C22⋊C4—5022no—
130C22⋊C4—5022no—
131C42—5022no—
132C42—5021no—
133C42C22×D25111yescharacteristic
134C23—21no—
135Q8—42no—
136Q8—10041no—
137Q8—10041no—
138Q8—5021no—
139Q8—5021no—
140D4—21no—
141D4—21no—
142C2×C4—21no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—5021no—
147C2×C4—5021no—
148C2×C4—5022no—
149C2×C4D4×D25111yescharacteristic
150C2×C4D4×D25111yescharacteristic
151C2×C4C2×C22⋊D25111yescharacteristic
152C8—41no—
153C8—10041no—
154C8—10041no—
155C22—41no—
156C22—41no—
157C22—41no—
158C22#2254868311yescharacteristic
159C4—21no—
160C4—41no—
161C4—81no—
162C4—10041no—
163C4—10042no—
164C4—10041no—
165C4#2254873511yescharacteristic
166C4#2254873611yescharacteristic
167C4#2254874411yescharacteristic
168C4#2254874611yescharacteristic
169C2—81no—
170C2#3063184611yescharacteristic
171C2#3063184711yescharacteristic
172C2#3063185811yescharacteristic
subgroupG/H
centerC22#22548683
commutator, cosocleC42×C251C23
FrattiniC42C22×D251
Fitting#476×C251C2
socleC22×C251#120
prime radicalC2×D4×C251D4
hypercenter#476D251
hypocenterC251#1638
LCSG ▷ C42×C251 ▷ C22×C251 ▷ C251
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
2. #30632037C2semidirect
3. #30631979C2semidirect
4. #30631434C2semidirect
5. #30631417C2semidirect
86. C251#1638semidirect

Maximal subgroups

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

subgroupindex
#306324072
#306320372
#306319792
#306314342
#306314172
D4⋊(C251⋊C8)2
#476×C2512
#1638251