Finite Group Databasebeta

← #44548770

Subgroups — #44548770

Order 32128.

212 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 65 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#30632219C211yesmaximal, characteristic
2#30631739C211yesmaximal, characteristic, complemented
3#30631738C211yesmaximal, characteristic, complemented
4#30631419C211yesmaximal, characteristic, complemented
5#30631417C211yesmaximal, characteristic, complemented
6D4⋊(C251⋊C8)C211yesmaximal, characteristic, complemented
7D4⋊C8×C251C211yesmaximal, characteristic, complemented
8#22548708—21no—
9#22548706C411yescharacteristic
10#22548702C411yescharacteristic
11#22548697—21no—
12#22548695C411yescharacteristic
13#22548686C411yescharacteristic
14C4×Dic502C2211yescharacteristic
15C4×C22⋊D251—21no—
16#22548674—21no—
17C42×D251C2211yescharacteristic
18C4⋊(C251⋊C8)C2211yescharacteristic
19Dic251⋊C8—21no—
20(C2×D251)⋊C8—21no—
21(C2×D251)⋊C8—21no—
22C4×C251⋊C8C2211yescharacteristic
23C8×Dic251—21no—
24C4×D4×C251C2211yescharacteristic
25C4⋊C8×C251C2211yescharacteristic
26C4×C8×C251C2211yescharacteristic
27C2×Dic502C2×C411yescharacteristic
28C2×C22⋊D251—21no—
29C2×C4×D251C2×C411yescharacteristic
30C2×C4×D251D411yescharacteristic
31C2×C4×D251D411yescharacteristic
32C2×C251⋊C8—21no—
33C2×C251⋊C8—21no—
34C4⋊Dic251—21no—
35C4⋊Dic251—21no—
36C4⋊Dic251C2×C411yescharacteristic
37Dic251⋊C4—21no—
38Dic251⋊C4—21no—
39C22⋊Dic251—21no—
40C22⋊Dic251—21no—
41C22⋊Dic251—21no—
42(C2×D251)⋊C4—21no—
43C4×Dic251—21no—
44C4×Dic251C2×C411yescharacteristic
45C4×Dic251D411yescharacteristic
46C4×Dic251D411yescharacteristic
47C2×D4×C251C2×C411yescharacteristic
48C22×C4×C251—21no—
49C2×C8×C251—21no—
50C2×C8×C251—21no—
51C4⋊C4×C251C2×C411yescharacteristic
52C22⋊C4×C251—21no—
53C42×C251C2311yescharacteristic
54C22×D251C22⋊C411yescharacteristic
55Dic502—21no—
56Dic502—21no—
57C22⋊D251—42no—
58C2×Dic251—21no—
59C2×Dic251—21no—
60C2×Dic251C22⋊C411yescharacteristic
61C2×Dic251C22⋊C411yescharacteristic
62C2×Dic251C22⋊C411yescharacteristic
63C4×D251—21no—
64C4×D251—21no—
65C4×D251—21no—
66C4×D251—21no—
67C4×D251—41no—
68C251⋊C8—41no—
69C251⋊C8—41no—
70C23×C251—21no—
71D4×C251—21no—
72D4×C251—21no—
73C2×C4×C251—21no—
74C2×C4×C251—41no—
75C2×C4×C251—41no—
76C2×C4×C251C22×C411yescharacteristic
77C2×C4×C251C2×D411yescharacteristic
78C2×C4×C251C2×D411yescharacteristic
79C8×C251—41no—
80C8×C251—41no—
81C22×C251—41no—
82C22×C251—41no—
83C22×C251—41no—
84C22×C251C2×C22⋊C411yescharacteristic
85C2×D251—21no—
86C2×D251—21no—
87C2×D251—21no—
88C4×C251—21no—
89C4×C251—41no—
90C4×C251#13111yescharacteristic
91C4×C251#13111yescharacteristic
92C4×C251#13511yescharacteristic
93C4×C251#13511yescharacteristic
94Dic251—21no—
95Dic251—21no—
96Dic251—21no—
97Dic251—41no—
98Dic251—41no—
99C2×C251—81no—
100C2×C251#40811yescharacteristic
101C2×C251#41611yescharacteristic
102C2×C251#42111yescharacteristic
103D251—41no—
104C251#148211yescharacteristic, complemented, Sylow
105#1482—2511nomaximal, Sylow
106#529—2511no—
107#431—2511no—
108#431—2511no—
109Q8⋊C8—2511no—
110Q8⋊C8—2511no—
111D4⋊C8—2511no—
112D4⋊C8D25111yescharacteristic, complemented
113#126—5021no—
114#125—2511no—
115#124—2511no—
116#123—5021no—
117C22⋊Q8—2511no—
118#121—2511no—
119C4×Q8—2511no—
120C4×D4—5021no—
121C4×D4C2×D25111yescharacteristic
122#117—5021no—
123C2×C42—2511no—
124C4⋊C8—5021no—
125C4⋊C8—2511no—
126C4⋊C8C2×D25111yescharacteristic
127C22⋊C8—5021no—
128C22⋊C8—5021no—
129C4×C8—5021no—
130C4×C8—2511no—
131C4×C8C2×D25111yescharacteristic
132C2×Q8—2511no—
133C2×D4—5021no—
134C2×D4C4×D25111yescharacteristic
135C22×C4—21no—
136C22×C4—2511no—
137C22×C4—2511no—
138C22×C4—2511no—
139C2×C8—21no—
140C2×C8—21no—
141C2×C8—5021no—
142C2×C8—5021no—
143C4⋊C4—5021no—
144C4⋊C4—5021no—
145C4⋊C4—5021no—
146C4⋊C4—5021no—
147C4⋊C4—2511no—
148C4⋊C4C4×D25111yescharacteristic
149C22⋊C4—21no—
150C22⋊C4—5021no—
151C22⋊C4—5021no—
152C22⋊C4—5021no—
153C22⋊C4—5021no—
154C42—5021no—
155C42—2511no—
156C42—2511no—
157C42—2511no—
158C42C22×D25111yescharacteristic
159C23—21no—
160C23—2511no—
161Q8—5021no—
162Q8—5021no—
163D4—21no—
164D4—21no—
165D4—10042no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—10041no—
170C2×C4—5021no—
171C2×C4—5021no—
172C2×C4—5021no—
173C2×C4—5021no—
174C2×C4—5021no—
175C2×C4—5021no—
176C2×C4—2511no—
177C2×C4—2511no—
178C2×C4—2511no—
179C2×C4C2×C4×D25111yescharacteristic
180C2×C4D4×D25111yescharacteristic
181C2×C4D4×D25111yescharacteristic
182C8—41no—
183C8—41no—
184C8—10041no—
185C8—10041no—
186C22—41no—
187C22—41no—
188C22—41no—
189C22—5021no—
190C22—5021no—
191C22—5021no—
192C22C22⋊C4×D25111yescharacteristic
193C4—21no—
194C4—41no—
195C4—10041no—
196C4—10041no—
197C4—5021no—
198C4—5021no—
199C4—5021no—
200C4#2254872111yescharacteristic
201C4#2254872311yescharacteristic
202C4#2254873411yescharacteristic
203C4#2254873611yescharacteristic
204C2—81no—
205C2—10041no—
206C2#3063165211yescharacteristic
207C2#3063168011yescharacteristic
208C2#3063170211yescharacteristic
subgroupG/H
centerC2×C4D4×D251
commutatorC2×C4×C251C22×C4
FrattiniC42C22×D251
FittingD4⋊C8×C251C2
socleC22×C251C2×C22⋊C4
prime radical#22548686C4
cosocleC42×C251C23
hypercenterD4⋊C8D251
hypocenterC251#1482
LCSG ▷ C2×C4×C251 ▷ C2×C251 ▷ C251
UCSC1 ◁ C2×C4 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #30631739C2semidirect
3. #30631738C2semidirect
4. #30631419C2semidirect
5. #30631417C2semidirect
6. D4⋊(C251⋊C8)C2semidirect
7. D4⋊C8×C251C2semidirect
104. C251#1482semidirect
112. D4⋊C8D251semidirect

Maximal subgroups

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

subgroupindex
#306322192
#306317392
#306317382
#306314192
#306314172
D4⋊(C251⋊C8)2
D4⋊C8×C2512
#1482251