Finite Group Databasebeta

← #44560496

Subgroups — #44560496

Order 32128.

380 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 129 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#30632244C211yesmaximal, characteristic
2C2×C4×Dic502C211yesmaximal, characteristic
3#30632018C212yesmaximal
4#30631973C212yesmaximal, complemented
5#30631898C212yesmaximal, complemented
6#30631845C212yesmaximal
7#30631795C214yesmaximal, complemented
8#432×C251C211yesmaximal, characteristic
9C22×Dic502C2211yescharacteristic
10C2×Dic1004C2214yes—
11#22548715C2211yescharacteristic
12#22548715C2211yescharacteristic
13#22548707—21no—
14#22548694—21no—
15#22548694C2212yes—
16C4×Dic502—21no—
17C4×Dic502—21no—
18C4×Dic502—21no—
19C4×Dic502C2212yes—
20C4×Dic502C2212yes—
21C4×Dic502C2212yes—
22#22548674—21no—
23C2×C4⋊Dic251C2211yescharacteristic
24C2×Dic251⋊C4—21no—
25C2×C4×Dic251—21no—
26#22548647C2214yes—
27#22548640C2214yes—
28#22548640C2214yes—
29C2×C42×C251C2211yescharacteristic
30C4⋊C8×C251C2212yes—
31C22⋊C8×C251C2212yes—
32#97×C251C2212yes—
33C2×Dic502—24no—
34C2×Dic502—21no—
35C2×Dic502—21no—
36C2×Dic502C2312yes—
37C2×Dic502C2312yes—
38C22×Dic251—21no—
39C22×Dic251—21no—
40Dic1004—28no—
41C4⋊Dic251—21no—
42C4⋊Dic251—21no—
43C4⋊Dic251—21no—
44C4⋊Dic251—21no—
45C4⋊Dic251C2312yes—
46C4⋊Dic251C2312yes—
47Dic251⋊C4—22no—
48Dic251⋊C4—22no—
49Dic251⋊C4—22no—
50Dic251⋊C4—22no—
51C22⋊Dic251—22no—
52C4×Dic251—22no—
53C4×Dic251—22no—
54C4×Dic251—22no—
55C22×C4×C251D411yescharacteristic
56C22×C4×C251D411yescharacteristic
57C22×C4×C251C2311yescharacteristic
58C2×C8×C251C2314yes—
59C42×C251D411yescharacteristic
60C42×C251D411yescharacteristic
61C42×C251C2311yescharacteristic
62C42×C251C2311yescharacteristic
63Dic502—24no—
64Dic502—22no—
65Dic502—24no—
66Dic502—42no—
67Dic502#4114yes—
68C2×Dic251—24no—
69C2×Dic251—22no—
70C2×Dic251—22no—
71C2×Dic251—22no—
72C2×Dic251—22no—
73C2×Dic251—42no—
74C23×C251C2×D411yescharacteristic
75C2×C4×C251—22no—
76C2×C4×C251—22no—
77C2×C4×C251—22no—
78C2×C4×C251C2×D411yescharacteristic
79C2×C4×C251C2×D411yescharacteristic
80C2×C4×C251C2×D411yescharacteristic
81C2×C4×C251C2×D411yescharacteristic
82C2×C4×C251C2×D411yescharacteristic
83C2×C4×C251C2411yescharacteristic
84C8×C251—24no—
85C22×C251—21no—
86C22×C251—21no—
87C22×C251#13712yes—
88C22×C251C22×D411yescharacteristic
89C4×C251—21no—
90C4×C251—21no—
91C4×C251—21no—
92C4×C251—21no—
93C4×C251#13712yes—
94C4×C251C2×#4112yes—
95Dic251—24no—
96Dic251—42no—
97Dic251—42no—
98Dic251—42no—
99C2×C251—22no—
100C2×C251#52511yescharacteristic
101C2×C251C2×#13711yescharacteristic
102C2×C251C2×#13711yescharacteristic
103C251#311311yescharacteristic, complemented, Sylow
104#3113—2511nomaximal, Sylow
105#533—2511no—
106C2×C4×Q8—2511no—
107#483—2512no—
108#475—2512no—
109#462—2512no—
110#451—2512no—
111#441—2514no—
112#432D25111yescharacteristic
113C22×Q8—2511no—
114C2×Q16—2514no—
115C4⋊Q8—2511no—
116C4⋊Q8—2511no—
117#125—5021no—
118C22⋊Q8—5021no—
119C22⋊Q8—2512no—
120C4×Q8—5021no—
121C4×Q8—5021no—
122C4×Q8—5021no—
123C4×Q8—2512no—
124C4×Q8—2512no—
125C4×Q8—2512no—
126#117—5021no—
127C2×C4⋊C4—5021no—
128C2×C4⋊C4—2511no—
129C2×C42—5021no—
130C2×C42C2×D25111yescharacteristic
131#106—2514no—
132C4⋊C8C2×D25112yes—
133#103—2514no—
134#103—2514no—
135C22⋊C8C2×D25112yes—
136#97C2×D25112yes—
137C2×Q8—5024no—
138C2×Q8—5021no—
139C2×Q8—5021no—
140C2×Q8—2512no—
141C2×Q8—2512no—
142C22×C4—5021no—
143C22×C4—5021no—
144C22×C4D100411yescharacteristic
145C22×C4D100411yescharacteristic
146C22×C4C22×D25111yescharacteristic
147Q16—5028no—
148C2×C8C22×D25114yes—
149C4⋊C4—5022no—
150C4⋊C4—5022no—
151C4⋊C4—5021no—
152C4⋊C4—5021no—
153C4⋊C4—5021no—
154C4⋊C4—5022no—
155C4⋊C4—5022no—
156C4⋊C4—5021no—
157C4⋊C4—2512no—
158C4⋊C4—2512no—
159C22⋊C4—5022no—
160C42—5022no—
161C42—5022no—
162C42—5022no—
163C42D100411yescharacteristic
164C42D100411yescharacteristic
165C42C22×D25111yescharacteristic
166C42C22×D25111yescharacteristic
167C23C2×D100411yescharacteristic
168Q8—10042no—
169Q8—5024no—
170Q8—5024no—
171Q8—5022no—
172Q8—2514no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—10042no—
177C2×C4—5022no—
178C2×C4—5022no—
179C2×C4—5022no—
180C2×C4—5024no—
181C2×C4—5022no—
182C2×C4C2×D100411yescharacteristic
183C2×C4C2×D100411yescharacteristic
184C2×C4C2×D100411yescharacteristic
185C2×C4C2×D100411yescharacteristic
186C2×C4C2×D100411yescharacteristic
187C2×C4C23×D25111yescharacteristic
188C8—24no—
189C22—21no—
190C22—21no—
191C22#2254874812yes—
192C22C22×D100411yescharacteristic
193C4—21no—
194C4—21no—
195C4—21no—
196C4—21no—
197C4—10042no—
198C4—10042no—
199C4—10042no—
200C4—5024no—
201C4#2254874812yes—
202C4#41×D25112yes—
203C2—22no—
204C2#3063219911yescharacteristic
205C2C2×#2254874811yescharacteristic
206C2C2×#2254874811yescharacteristic
subgroupG/H
centerC22C22×D1004
commutator, cosocleC2×C4×C251C24
FrattiniC2×C4C23×D251
Fitting#432×C251C2
socleC22×C251C22×D4
prime radicalC23×C251C2×D4
hypercenter#432D251
hypocenterC251#3113
LCSG ▷ C2×C4×C251 ▷ C2×C251 ▷ C251
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
4. #30631973C2semidirect
5. #30631898C2semidirect
7. #30631795C2semidirect
103. C251#3113semidirect

Maximal subgroups

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

subgroupindex
#306322442
C2×C4×Dic5022
#306320182
#306319732
#306318982
#306318452
#306317952
#432×C2512
#3113251