Finite Group Databasebeta

← #44549013

Subgroups — #44549013

Order 32128.

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

normal subgroups only

This group has 256 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#30632238C211yesmaximal, characteristic
2#30631739C211yesmaximal, characteristic, complemented
3C4⋊C8×D251C211yesmaximal, characteristic, complemented
4#30631433C211yesmaximal, characteristic, complemented
5#30631430C211yesmaximal, characteristic, complemented
6#30631430C211yesmaximal, characteristic, complemented
7#332×C251C211yesmaximal, characteristic, complemented
8C2×#16860811—21no—
9C2×C8×D251—21no—
10#22548712C2211yescharacteristic
11#22548704—21no—
12#22548690—21no—
13#22548690C412yes—
14#22548677—21no—
15#22548677C412yes—
16C42×D251C2211yescharacteristic
17C4⋊(C251⋊C8)C2211yescharacteristic
18C4⋊(C251⋊C8)C2211yescharacteristic
19Dic251⋊C8—21no—
20(C2×D251)⋊C8—21no—
21C8×Dic251—21no—
22C4⋊Q8×C251C2211yescharacteristic
23C4⋊C8×C251C2211yescharacteristic
24C4⋊C8×C251C2211yescharacteristic
25#16860811—42no—
26#16860811—42no—
27C2×D1004—22no—
28C2×D1004—21no—
29C2×D1004—21no—
30C2×D1004C2×C412yes—
31C2×C4×D251—22no—
32C2×C4×D251C2×C411yescharacteristic
33C2×C4×D251D411yescharacteristic
34C2×C4×D251D411yescharacteristic
35C2×C251⋊C8—21no—
36C2×C251⋊C8—21no—
37C8×D251—42no—
38(C2×D251)⋊C4—22no—
39(C2×D251)⋊C4—22no—
40C4×Dic251C2×C411yescharacteristic
41C4×Dic251D411yescharacteristic
42C4×Dic251D411yescharacteristic
43C2×Q8×C251—21no—
44C2×C8×C251—21no—
45C2×C8×C251—21no—
46C4⋊C4×C251—21no—
47C4⋊C4×C251C2×C412yes—
48C42×C251C2311yescharacteristic
49C22×D251—22no—
50C22×D251C22⋊C411yescharacteristic
51D1004—42no—
52D1004—44no—
53D1004—41no—
54D1004—41no—
55D1004—41no—
56D1004—41no—
57C2×Dic251C22⋊C411yescharacteristic
58C2×Dic251C22⋊C411yescharacteristic
59C2×Dic251C22⋊C411yescharacteristic
60C4×D251—21no—
61C4×D251—21no—
62C4×D251—41no—
63C4×D251—44no—
64C4×D251D812yes—
65C4×D251SD1612yes—
66C251⋊C8—41no—
67C251⋊C8—41no—
68Q8×C251—41no—
69Q8×C251—41no—
70C2×C4×C251—22no—
71C2×C4×C251C22×C411yescharacteristic
72C2×C4×C251C2×D411yescharacteristic
73C2×C4×C251C2×D411yescharacteristic
74C8×C251—41no—
75C8×C251—41no—
76C22×C251C2×C22⋊C411yescharacteristic
77C2×D251—21no—
78C2×D251—21no—
79C2×D251—42no—
80C2×D251—42no—
81C2×D251—42no—
82C2×D251#10212yes—
83C4×C251—21no—
84C4×C251—42no—
85C4×C251C2×D811yescharacteristic
86C4×C251C2×SD1611yescharacteristic
87C4×C251#13511yescharacteristic
88C4×C251#13511yescharacteristic
89Dic251—21no—
90Dic251—21no—
91Dic251#10212yes—
92C2×C251#41311yescharacteristic
93C2×C251C2×#10211yescharacteristic
94C2×C251#41611yescharacteristic
95D251—22no—
96D251—82no—
97C251#154011yescharacteristic, complemented, Sylow
98#1540—2511nomaximal, Sylow
99#532—2511no—
100#431—2511no—
101C2×C4⋊C8—2511no—
102#332—2511no—
103#332D25111yescharacteristic, complemented
104#331—2511no—
105#331—2511no—
106C2×#41—5021no—
107C22×C8—5021no—
108C4⋊Q8C2×D25111yescharacteristic
109#127—2511no—
110#124—5021no—
111#121—5021no—
112#121—2512no—
113C4×D4—5021no—
114C4×D4—2512no—
115C2×C42—2511no—
116C4⋊C8—5021no—
117C4⋊C8—2511no—
118C4⋊C8—2511no—
119C4⋊C8C2×D25111yescharacteristic
120C4⋊C8C2×D25111yescharacteristic
121C22⋊C8—5021no—
122C4×C8—5021no—
123#41—10042no—
124#41—10042no—
125C2×Q8—21no—
126C2×D4—5022no—
127C2×D4—5021no—
128C2×D4—5021no—
129C2×D4—2512no—
130C22×C4—5022no—
131C22×C4—2511no—
132C22×C4—2511no—
133C22×C4—2511no—
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—10042no—
137C2×C8—5021no—
138C2×C8—5021no—
139C4⋊C4—21no—
140C4⋊C4C4×D25112yes—
141C22⋊C4—5022no—
142C22⋊C4—5022no—
143C42—2511no—
144C42—2511no—
145C42—2511no—
146C42C22×D25111yescharacteristic
147C23—5022no—
148C23—2511no—
149Q8—41no—
150Q8—41no—
151D4—10042no—
152D4—10044no—
153D4—10041no—
154D4—10041no—
155D4—10041no—
156D4—10041no—
157C2×C4—22no—
158C2×C4—10041no—
159C2×C4—10044no—
160C2×C4—5021no—
161C2×C4—5021no—
162C2×C4—2511no—
163C2×C4—2511no—
164C2×C4—2511no—
165C2×C4—2512no—
166C2×C4—2512no—
167C2×C4C2×C4×D25111yescharacteristic
168C2×C4D4×D25111yescharacteristic
169C2×C4D4×D25111yescharacteristic
170C8—41no—
171C8—41no—
172C8—10041no—
173C8—10041no—
174C22—10042no—
175C22—10042no—
176C22—10042no—
177C22—5021no—
178C22—5021no—
179C22—2512no—
180C22C22⋊C4×D25111yescharacteristic
181C4—21no—
182C4—42no—
183C4—5021no—
184C4—5021no—
185C4—2512no—
186C4D8×D25111yescharacteristic
187C4SD16×D25111yescharacteristic
188C4#2254873611yescharacteristic
189C4#2254873811yescharacteristic
190C2—20082no—
191C2—5022no—
192C2#3063167011yescharacteristic
193C2#102×D25111yescharacteristic
194C2#3063168211yescharacteristic
subgroupG/H
centerC22C22⋊C4×D251
commutatorC2×C4×C251C22×C4
FrattiniC42C22×D251
Fitting#332×C251C2
socleC22×C251C2×C22⋊C4
prime radical#30632238C2
cosocleC42×C251C23
hypercenter#332D251
hypocenterC251#1540
LCSG ▷ C2×C4×C251 ▷ C22×C251 ▷ C251
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #30631739C2semidirect
3. C4⋊C8×D251C2semidirect
4. #30631433C2semidirect
5. #30631430C2semidirect
6. #30631430C2semidirect
7. #332×C251C2semidirect
97. C251#1540semidirect
103. #332D251semidirect

Maximal subgroups

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

subgroupindex
#306322382
#306317392
C4⋊C8×D2512
#306314332
#306314302
#332×C2512
#1540251