Finite Group Databasebeta

← #44549059

Subgroups — #44549059

Order 32128.

252 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 67 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#30632238C211yesmaximal, characteristic
2#30631743C211yesmaximal, characteristic, complemented
3C4⋊C8×D251C211yesmaximal, characteristic, complemented
4#30631436C211yesmaximal, characteristic, complemented
5#30631430C211yesmaximal, characteristic, complemented
6#30631430C211yesmaximal, characteristic, complemented
7#333×C251C211yesmaximal, characteristic, complemented
8C2×#16860811C412yes—
9C2×C8×D251—21no—
10#22548712C2211yescharacteristic
11#22548704C412yes—
12#22548690—21no—
13#22548690—21no—
14#22548677—21no—
15#22548677—21no—
16C42×D251C2211yescharacteristic
17C4⋊(C251⋊C8)C2211yescharacteristic
18C4⋊(C251⋊C8)C2211yescharacteristic
19Dic251⋊C8—21no—
20(C2×D251)⋊C8—21no—
21#22548625—21no—
22C4⋊Q8×C251C2211yescharacteristic
23C4⋊C8×C251C2211yescharacteristic
24C4⋊C8×C251C2211yescharacteristic
25#16860811—44no—
26C2×D1004—22no—
27C2×D1004—21no—
28C2×D1004—21no—
29C2×D1004C2×C412yes—
30C2×C4×D251—22no—
31C2×C4×D251C2×C411yescharacteristic
32C2×C4×D251D411yescharacteristic
33C2×C4×D251D411yescharacteristic
34C2×C251⋊C8—21no—
35C2×C251⋊C8—21no—
36C8×D251—42no—
37(C2×D251)⋊C4—22no—
38(C2×D251)⋊C4—22no—
39C4×Dic251C2×C411yescharacteristic
40C4×Dic251D411yescharacteristic
41C4×Dic251D411yescharacteristic
42C2×Q8×C251C2×C412yes—
43C2×C8×C251—21no—
44C2×C8×C251—21no—
45C4⋊C4×C251—21no—
46C4⋊C4×C251—21no—
47C42×C251C2311yescharacteristic
48C22×D251—22no—
49C22×D251C22⋊C411yescharacteristic
50D1004—42no—
51D1004—44no—
52D1004—41no—
53D1004—41no—
54D1004—41no—
55D1004—41no—
56C2×Dic251C22⋊C411yescharacteristic
57C2×Dic251C22⋊C411yescharacteristic
58C2×Dic251C22⋊C411yescharacteristic
59C4×D251—22no—
60C4×D251—21no—
61C4×D251—21no—
62C4×D251—21no—
63C4×D251—21no—
64C4×D251—44no—
65C251⋊C8—41no—
66C251⋊C8—41no—
67Q8×C251—42no—
68C2×C4×C251—22no—
69C2×C4×C251C22×C411yescharacteristic
70C2×C4×C251C2×D411yescharacteristic
71C2×C4×C251C2×D411yescharacteristic
72C8×C251—41no—
73C8×C251—41no—
74C22×C251C2×C22⋊C411yescharacteristic
75C2×D251—21no—
76C2×D251—21no—
77C2×D251—42no—
78C2×D251—42no—
79C2×D251—42no—
80C2×D251#10012yes—
81C4×C251—21no—
82C4×C251—42no—
83C4×C251#13511yescharacteristic
84C4×C251#13511yescharacteristic
85C4×C251AGL(1,ℤ/8)11yescharacteristic
86C4×C251#13711yescharacteristic
87Dic251—21no—
88Dic251—21no—
89Dic251—21no—
90C2×C251C2×#10011yescharacteristic
91C2×C251#41611yescharacteristic
92C2×C251#41711yescharacteristic
93D251—22no—
94D251—82no—
95C251#155111yescharacteristic, complemented, Sylow
96#1551—2511nomaximal, Sylow
97#532—2511no—
98#432—2511no—
99C2×C4⋊C8—2511no—
100#333—2511no—
101#333D25111yescharacteristic, complemented
102#331—2511no—
103#331—2511no—
104C2×#41—2512no—
105C22×C8—5021no—
106C4⋊Q8C2×D25111yescharacteristic
107#127—2511no—
108#124—2512no—
109#121—5021no—
110#121—5021no—
111C4×D4—5021no—
112C4×D4—5021no—
113C2×C42—2511no—
114C4⋊C8—5021no—
115C4⋊C8—2511no—
116C4⋊C8—2511no—
117C4⋊C8C2×D25111yescharacteristic
118C4⋊C8C2×D25111yescharacteristic
119C22⋊C8—5021no—
120#97—5021no—
121#41—10044no—
122C2×Q8C4×D25112yes—
123C2×D4—5022no—
124C2×D4—5021no—
125C2×D4—5021no—
126C2×D4—2512no—
127C22×C4—5022no—
128C22×C4—2511no—
129C22×C4—2511no—
130C22×C4—2511no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—10042no—
134C2×C8—5021no—
135C2×C8—5021no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C22⋊C4—5022no—
139C22⋊C4—5022no—
140C42—2511no—
141C42—2511no—
142C42—2511no—
143C42C22×D25111yescharacteristic
144C23—5022no—
145C23—2511no—
146Q8—42no—
147D4—10042no—
148D4—10044no—
149D4—10041no—
150D4—10041no—
151D4—10041no—
152D4—10041no—
153C2×C4—22no—
154C2×C4—10044no—
155C2×C4—5022no—
156C2×C4—5021no—
157C2×C4—5021no—
158C2×C4—5021no—
159C2×C4—5021no—
160C2×C4—2511no—
161C2×C4—2511no—
162C2×C4—2511no—
163C2×C4C2×C4×D25111yescharacteristic
164C2×C4D4×D25111yescharacteristic
165C2×C4D4×D25111yescharacteristic
166C8—41no—
167C8—41no—
168C8—10041no—
169C8—10041no—
170C22—10042no—
171C22—10042no—
172C22—10042no—
173C22—5021no—
174C22—5021no—
175C22—2512no—
176C22C22⋊C4×D25111yescharacteristic
177C4—21no—
178C4—42no—
179C4—5021no—
180C4—5021no—
181C4—5021no—
182C4#2254873611yescharacteristic
183C4#2254873811yescharacteristic
184C4#2254874211yescharacteristic
185C4#2254874711yescharacteristic
186C2—20082no—
187C2—5022no—
188C2#100×D25111yescharacteristic
189C2#3063168211yescharacteristic
190C2#3063168711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D251
commutatorC2×C4×C251C22×C4
FrattiniC42C22×D251
Fitting#333×C251C2
socleC22×C251C2×C22⋊C4
prime radical#30632238C2
cosocleC42×C251C23
hypercenter#333D251
hypocenterC251#1551
LCSG ▷ C2×C4×C251 ▷ C22×C251 ▷ C251
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
2. #30631743C2semidirect
3. C4⋊C8×D251C2semidirect
4. #30631436C2semidirect
5. #30631430C2semidirect
6. #30631430C2semidirect
7. #333×C251C2semidirect
95. C251#1551semidirect
101. #333D251semidirect

Maximal subgroups

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

subgroupindex
#306322382
#306317432
C4⋊C8×D2512
#306314362
#306314302
#333×C2512
#1551251