Finite Group Databasebeta

← #44550467

Subgroups — #44550467

Order 32128.

262 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 73 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#30632155C211yesmaximal, characteristic
2#30631669C211yesmaximal, characteristic
3#30631660C211yesmaximal, characteristic
4#30631448C211yesmaximal, characteristic, complemented
5#30631446C211yesmaximal, characteristic, complemented
6#30631443C211yesmaximal, characteristic, complemented
7H(3,ℤ/4)×C251C211yesmaximal, characteristic, complemented
8C2×#16860810C2211yescharacteristic
9C2×#16860794C2211yescharacteristic
10#22548680—21no—
11#22548677—21no—
12(C22⋊D251)⋊C4—22no—
13#22548674C2211yescharacteristic
14#22548672C412yescomplemented
15C2×C4×Dic251C2211yescharacteristic
16C42×D251C412yescomplemented
17#22548633—21no—
18#22548631—21no—
19#22548629—22no—
20C2×M16×C251C2211yescharacteristic
21#117×C251C2211yescharacteristic
22#117×C251C2211yescharacteristic
23#16860810—21no—
24#16860810—21no—
25#16860810—21no—
26#16860810—21no—
27C2×Dic502D411yescharacteristic
28C2×D1004D411yescharacteristic
29C2×C22⋊D251D412yes—
30C22×Dic251—21no—
31C2×C4×D251—22no—
32C2×C4×D251C2×C412yes—
33#16860794—21no—
34#16860794—21no—
35C2×C251⋊C8—21no—
36C4⋊Dic251—21no—
37Dic251⋊C4—22no—
38C22⋊Dic251—21no—
39(C2×D251)⋊C4—22no—
40C4×Dic251—22no—
41C4×Dic251—21no—
42C4×Dic251—21no—
43C4×Dic251C2×C411yescharacteristic
44C4×Dic251C2×C411yescharacteristic
45C22×C4×C251C2311yescharacteristic
46M16×C251—21no—
47M16×C251—21no—
48C2×C8×C251—21no—
49C4⋊C4×C251—21no—
50C4⋊C4×C251—21no—
51C22⋊C4×C251—21no—
52C22⋊C4×C251—21no—
53C42×C251—21no—
54C42×C251C2×C412yes—
55C22×D251C22⋊C412yes—
56Dic502—21no—
57Dic502—21no—
58D1004—21no—
59D1004—21no—
60C22⋊D251—22no—
61C22⋊D251—22no—
62C2×Dic251—21no—
63C2×Dic251—21no—
64C2×Dic251—42no—
65C2×Dic251—41no—
66C2×Dic251C22⋊C412yes—
67C4×D251—22no—
68C4×D251—22no—
69C4×D251—44no—
70C251⋊C8—41no—
71C23×C251C2×D411yescharacteristic
72C2×C4×C251—22no—
73C2×C4×C251—41no—
74C2×C4×C251C22×C411yescharacteristic
75C2×C4×C251C2×D411yescharacteristic
76C2×C4×C251#4111yescharacteristic
77C2×C4×C251#4111yescharacteristic
78C2×C4×C251#4111yescharacteristic
79C2×C4×C251#4111yescharacteristic
80C8×C251—41no—
81C22×C251—41no—
82C22×C251C2×C22⋊C411yescharacteristic
83C22×C251#12311yescharacteristic
84C22×C251#12311yescharacteristic
85C2×D251—22no—
86C2×D251—42no—
87C4×C251—42no—
88C4×C251—81no—
89C4×C251#11711yescharacteristic
90C4×C251#11711yescharacteristic
91C4×C251#12311yescharacteristic
92C4×C251#12311yescharacteristic
93Dic251—22no—
94Dic251—22no—
95Dic251—41no—
96Dic251—81no—
97C2×C251—21no—
98C2×C251—21no—
99C2×C251—21no—
100C2×C251#38111yescharacteristic
101D251—42no—
102C251#182711yescharacteristic, complemented, Sylow
103#1827—2511nomaximal, Sylow
104C4×#41—2511no—
105#413—2511no—
106#410—2511no—
107#339—2511no—
108#339—2511no—
109H(3,ℤ/4)—2511no—
110H(3,ℤ/4)D25111yescharacteristic, complemented
111C2×#41—2511no—
112C2×M16—2511no—
113C2×M16C2×D25111yescharacteristic
114C4×Q8—5021no—
115C4×D4—5022no—
116C4×D4—5021no—
117#117—2511no—
118#117—2512no—
119#117C2×D25111yescharacteristic
120#117C2×D25111yescharacteristic
121C2×C42—2511no—
122C2×C42—2512no—
123#101—5021no—
124#100—5021no—
125#99—5022no—
126#41—5021no—
127#41—5021no—
128#41—5021no—
129#41—5021no—
130C2×Q8—2511no—
131C2×D4—2512no—
132C2×D4—2511no—
133C22×C4—5022no—
134C22×C4—5021no—
135C22×C4—2512no—
136C22×C4C22×D25111yescharacteristic
137M16—21no—
138M16—21no—
139M16—5021no—
140M16—5021no—
141C2×C8—21no—
142C2×C8—5021no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—5022no—
146C4⋊C4—5021no—
147C22⋊C4—21no—
148C22⋊C4—21no—
149C22⋊C4—5022no—
150C22⋊C4—5021no—
151C42—21no—
152C42—5022no—
153C42—5021no—
154C42—5021no—
155C42—2511no—
156C42—2511no—
157C42C4×D25112yes—
158C23—2512no—
159C23D4×D25111yescharacteristic
160Q8—5021no—
161Q8—5021no—
162D4—5022no—
163D4—5022no—
164D4—5021no—
165D4—5021no—
166C2×C4—22no—
167C2×C4—41no—
168C2×C4—10044no—
169C2×C4—10041no—
170C2×C4—10042no—
171C2×C4—5021no—
172C2×C4—5021no—
173C2×C4—5022no—
174C2×C4—5022no—
175C2×C4—2512no—
176C2×C4C2×C4×D25111yescharacteristic
177C2×C4D4×D25111yescharacteristic
178C2×C4#1686080911yescharacteristic
179C2×C4#1686081011yescharacteristic
180C2×C4#1686081011yescharacteristic
181C2×C4#1686081111yescharacteristic
182C8—41no—
183C8—10041no—
184C22—41no—
185C22—10042no—
186C22—5022no—
187C22C22⋊C4×D25111yescharacteristic
188C22#2254869711yescharacteristic
189C22#2254870011yescharacteristic
190C4—42no—
191C4—81no—
192C4—20081no—
193C4—10041no—
194C4—5022no—
195C4—5022no—
196C4#2254867211yescharacteristic
197C4#2254867311yescharacteristic
198C4#2254869711yescharacteristic
199C4#2254870011yescharacteristic
200C2—21no—
201C2—21no—
202C2—21no—
203C2—10042no—
204C2#3063154911yescharacteristic
subgroupG/H
centerC4#22548672
commutatorC2×C4×C251C22×C4
FrattiniC22×C4C22×D251
FittingH(3,ℤ/4)×C251C2
socleC2×C251#381
prime radicalC2×#16860810C22
cosocleC22×C4×C251C23
hypercenterH(3,ℤ/4)D251
hypocenterC251#1827
LCSG ▷ C2×C4×C251 ▷ C2×C251 ▷ C251
UCSC1 ◁ C4 ◁ #117 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
4. #30631448C2semidirect
5. #30631446C2semidirect
6. #30631443C2semidirect
7. H(3,ℤ/4)×C251C2semidirect
14. #22548672C4semidirect
16. C42×D251C4semidirect
102. C251#1827semidirect
110. H(3,ℤ/4)D251semidirect

Maximal subgroups

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

subgroupindex
#306321552
#306316692
#306316602
#306314482
#306314462
#306314432
H(3,ℤ/4)×C2512
#1827251