Finite Group Databasebeta

← #44550860

Subgroups — #44550860

Order 32128.

310 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 79 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
1C2×#22548748C211yesmaximal, characteristic
2#30632164C211yesmaximal, characteristic, complemented
3#30631705C211yesmaximal, characteristic
4#30631695C211yesmaximal, characteristic, complemented
5#30631660C211yesmaximal, characteristic
6#30631458C211yesmaximal, characteristic, complemented
7H(3,ℤ/4)×C251C211yesmaximal, characteristic, complemented
8C2×#16860810C2211yescharacteristic
9C22×Dic502C2211yescharacteristic
10#22548748—22no—
11#22548748—22no—
12C2×Dic1004C412yescomplemented
13C2×#16860799C412yescomplemented
14C2×#16860794C2211yescharacteristic
15C4×Dic502—22no—
16#22548680—22no—
17#22548674C2211yescharacteristic
18#22548671—22no—
19#22548643—22no—
20#22548638—22no—
21#22548629—22no—
22C2×M16×C251C2211yescharacteristic
23#117×C251C2211yescharacteristic
24#117×C251C2211yescharacteristic
25#16860810—21no—
26#16860810—21no—
27#16860810—21no—
28#16860810—21no—
29C2×Dic502—21no—
30C2×Dic502—21no—
31C2×Dic502—21no—
32C2×Dic502C2×C411yescharacteristic
33C2×Dic502C2×C412yes—
34C2×Dic502D412yes—
35C2×Dic502D412yes—
36C2×D1004C2×C411yescharacteristic
37C2×C22⋊D251—21no—
38C22×Dic251—21no—
39C2×C4×D251—21no—
40Dic1004—24no—
41#16860799—24no—
42#16860794—21no—
43#16860794—21no—
44C2×C251⋊C8—21no—
45C4⋊Dic251—21no—
46Dic251⋊C4—24no—
47C22⋊Dic251D412yes—
48C4×Dic251—24no—
49C4×Dic251—21no—
50C22×C4×C251C2311yescharacteristic
51M16×C251—21no—
52M16×C251—21no—
53C2×C8×C251C2×C412yes—
54C4⋊C4×C251—21no—
55C4⋊C4×C251—21no—
56C22⋊C4×C251—21no—
57C22⋊C4×C251—21no—
58C42×C251—21no—
59C42×C251D412yes—
60C22×D251—21no—
61Dic502—22no—
62Dic502—22no—
63Dic502—22no—
64Dic502—21no—
65Dic502—21no—
66Dic502C22⋊C414yes—
67D1004—21no—
68D1004—21no—
69C22⋊D251—41no—
70C22⋊D251—41no—
71C2×Dic251—22no—
72C2×Dic251—22no—
73C2×Dic251—22no—
74C2×Dic251—21no—
75C2×Dic251—22no—
76C4×D251—41no—
77C4×D251—41no—
78C251⋊C8—41no—
79C23×C251C2×D411yescharacteristic
80C2×C4×C251—22no—
81C2×C4×C251—41no—
82C2×C4×C251C22×C411yescharacteristic
83C2×C4×C251C2×D411yescharacteristic
84C2×C4×C251C2×D411yescharacteristic
85C2×C4×C251C2×D411yescharacteristic
86C2×C4×C251#4111yescharacteristic
87C2×C4×C251#4111yescharacteristic
88C8×C251—22no—
89C22×C251—41no—
90C22×C251C4×D411yescharacteristic
91C22×C251#12011yescharacteristic
92C22×C251#12111yescharacteristic
93C2×D251—41no—
94C2×D251—81no—
95C4×C251—42no—
96C4×C251—81no—
97C4×C251C2×C22⋊C411yescharacteristic
98C4×C251C4×D411yescharacteristic
99C4×C251#12111yescharacteristic
100C4×C251#12311yescharacteristic
101Dic251—24no—
102Dic251—42no—
103Dic251—41no—
104C2×C251—21no—
105C2×C251—21no—
106C2×C251—21no—
107C2×C251#38611yescharacteristic
108D251—81no—
109C251#190511yescharacteristic, complemented, Sylow
110#1905—2511nomaximal, Sylow
111C2×#137—2511no—
112#519—2511no—
113#421—2511no—
114#419—2511no—
115#410—2511no—
116#344—2511no—
117H(3,ℤ/4)D25111yescharacteristic, complemented
118C2×#41—2511no—
119C22×Q8—2511no—
120#137—5022no—
121#137—5022no—
122C2×Q16—2512no—
123C2×SD16—2512no—
124C2×M16—2511no—
125C2×M16C2×D25111yescharacteristic
126C4×Q8—5022no—
127C4×Q8—5022no—
128#117—5022no—
129#117—2511no—
130#117C2×D25111yescharacteristic
131#117C2×D25111yescharacteristic
132#104—5022no—
133#103—5022no—
134#99—5022no—
135#41—5021no—
136#41—5021no—
137#41—5021no—
138#41—5021no—
139C2×Q8—5021no—
140C2×Q8—5021no—
141C2×Q8—5021no—
142C2×Q8—2511no—
143C2×Q8—2512no—
144C2×Q8—2512no—
145C2×Q8—2512no—
146C2×D4—5021no—
147C2×D4—2511no—
148C22×C4—5021no—
149C22×C4—5021no—
150C22×C4C22×D25111yescharacteristic
151Q16—5024no—
152SD16—5024no—
153M16—21no—
154M16—21no—
155M16—5021no—
156M16—5021no—
157C2×C8—5021no—
158C2×C8C4×D25112yes—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—5024no—
162C4⋊C4—5021no—
163C22⋊C4—21no—
164C22⋊C4—21no—
165C22⋊C4—2512no—
166C42—21no—
167C42—5024no—
168C42—5021no—
169C42D100412yes—
170C23—5021no—
171C23D4×D25111yescharacteristic
172Q8—5021no—
173Q8—5021no—
174Q8—5022no—
175Q8—5022no—
176Q8—5022no—
177Q8—2514no—
178D4—10041no—
179D4—10041no—
180D4—5021no—
181D4—5021no—
182C2×C4—22no—
183C2×C4—41no—
184C2×C4—10041no—
185C2×C4—10041no—
186C2×C4—5021no—
187C2×C4—5022no—
188C2×C4—5022no—
189C2×C4—5022no—
190C2×C4—5022no—
191C2×C4C2×C4×D25111yescharacteristic
192C2×C4D4×D25111yescharacteristic
193C2×C4D4×D25111yescharacteristic
194C2×C4C2×D100411yescharacteristic
195C2×C4#1686081011yescharacteristic
196C2×C4#1686081111yescharacteristic
197C8—22no—
198C8—10041no—
199C22—41no—
200C22—20081no—
201C22—10041no—
202C22#2254867711yescharacteristic
203C22#2254868511yescharacteristic
204C22#2254868811yescharacteristic
205C4—42no—
206C4—81no—
207C4—10042no—
208C4—10041no—
209C4—5024no—
210C4C22⋊C4×D25111yescharacteristic
211C4C4×D100411yescharacteristic
212C4#2254869011yescharacteristic
213C4#2254870011yescharacteristic
214C2—21no—
215C2—21no—
216C2—21no—
217C2—20081no—
218C2#3063156511yescharacteristic
subgroupG/H
centerC2#30631565
commutatorC2×C4×C251C22×C4
FrattiniC22×C4C22×D251
FittingH(3,ℤ/4)×C251C2
socleC2×C251#386
prime radicalC2×#16860810C22
cosocleC22×C4×C251C23
hypercenterH(3,ℤ/4)D251
hypocenterC251#1905
LCSG ▷ C2×C4×C251 ▷ C2×C251 ▷ C251
UCSC1 ◁ C2 ◁ C22×C4 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
2. #30632164C2semidirect
4. #30631695C2semidirect
6. #30631458C2semidirect
7. H(3,ℤ/4)×C251C2semidirect
12. C2×Dic1004C4semidirect
13. C2×#16860799C4semidirect
109. C251#1905semidirect
117. 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
C2×#225487482
#306321642
#306317052
#306316952
#306316602
#306314582
H(3,ℤ/4)×C2512
#1905251