Finite Group Databasebeta

← #44548822

Subgroups — #44548822

Order 32128.

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

normal subgroups only

This group has 230 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#30632219C211yesmaximal, characteristic
2#30631743C211yesmaximal, characteristic, complemented
3C4×C8×D251C211yesmaximal, characteristic, complemented
4#30631419C211yesmaximal, characteristic, complemented
5#30631417C211yesmaximal, characteristic, complemented
6D4⋊(C251⋊C8)C211yesmaximal, characteristic, complemented
7D4⋊C8×C251C211yesmaximal, characteristic, complemented
8C2×C8×D251—21no—
9#22548708—21no—
10#22548706C411yescharacteristic
11#22548702C411yescharacteristic
12#22548697—21no—
13#22548695C411yescharacteristic
14#22548686C411yescharacteristic
15C4×Dic502C2211yescharacteristic
16C4×C22⋊D251—21no—
17#22548674—21no—
18C42×D251C2211yescharacteristic
19C4⋊(C251⋊C8)C2211yescharacteristic
20(C2×D251)⋊C8—21no—
21#22548625—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—
34C8×D251—24no—
35C4⋊Dic251—21no—
36C4⋊Dic251—21no—
37C4⋊Dic251C2×C411yescharacteristic
38Dic251⋊C4—21no—
39Dic251⋊C4—21no—
40C22⋊Dic251—21no—
41C22⋊Dic251—21no—
42C22⋊Dic251—21no—
43(C2×D251)⋊C4—21no—
44C4×Dic251—21no—
45C4×Dic251C2×C411yescharacteristic
46C4×Dic251D411yescharacteristic
47C4×Dic251D411yescharacteristic
48C2×D4×C251C2×C411yescharacteristic
49C22×C4×C251—21no—
50C2×C8×C251—21no—
51C2×C8×C251—21no—
52C4⋊C4×C251C2×C411yescharacteristic
53C22⋊C4×C251—21no—
54C42×C251C2311yescharacteristic
55C22×D251C22⋊C411yescharacteristic
56Dic502—21no—
57Dic502—21no—
58C22⋊D251—42no—
59C2×Dic251—21no—
60C2×Dic251—21no—
61C2×Dic251C22⋊C411yescharacteristic
62C2×Dic251C22⋊C411yescharacteristic
63C2×Dic251C22⋊C411yescharacteristic
64C4×D251—22no—
65C4×D251—21no—
66C4×D251—21no—
67C4×D251—21no—
68C4×D251—21no—
69C251⋊C8—22no—
70C251⋊C8—41no—
71C23×C251—21no—
72D4×C251—21no—
73D4×C251—21no—
74C2×C4×C251—21no—
75C2×C4×C251—41no—
76C2×C4×C251—41no—
77C2×C4×C251C22×C411yescharacteristic
78C2×C4×C251C2×D411yescharacteristic
79C2×C4×C251C2×D411yescharacteristic
80C8×C251—22no—
81C8×C251—41no—
82C22×C251—41no—
83C22×C251—41no—
84C22×C251—41no—
85C22×C251C2×C22⋊C411yescharacteristic
86C2×D251—21no—
87C2×D251—21no—
88C2×D251#10412yes—
89C4×C251—21no—
90C4×C251—41no—
91C4×C251#13111yescharacteristic
92C4×C251#13111yescharacteristic
93C4×C251#13511yescharacteristic
94C4×C251#13511yescharacteristic
95Dic251—21no—
96Dic251—21no—
97Dic251—21no—
98Dic251—41no—
99Dic251—41no—
100C2×C251—81no—
101C2×C251#40811yescharacteristic
102C2×C251#41611yescharacteristic
103C2×C251C2×#10411yescharacteristic
104D251—22no—
105C251#149411yescharacteristic, complemented, Sylow
106#1494—2511nomaximal, Sylow
107#529—2511no—
108#432—2511no—
109C2×C4×C8—2511no—
110Q8⋊C8—2511no—
111Q8⋊C8—2511no—
112D4⋊C8—2511no—
113D4⋊C8D25111yescharacteristic, complemented
114C22×C8—5021no—
115#126—5021no—
116#125—2511no—
117#124—2511no—
118#123—5021no—
119C22⋊Q8—2511no—
120#121—2511no—
121C4×Q8—2511no—
122C4×D4—5021no—
123C4×D4C2×D25111yescharacteristic
124#117—5021no—
125C2×C42—2511no—
126C4⋊C8—2511no—
127C4⋊C8C2×D25111yescharacteristic
128C22⋊C8—5021no—
129#97—5021no—
130C4×C8—5021no—
131C4×C8—2511no—
132C4×C8C2×D25111yescharacteristic
133C2×Q8—2511no—
134C2×D4—5021no—
135C2×D4C4×D25111yescharacteristic
136C22×C4—21no—
137C22×C4—2511no—
138C22×C4—2511no—
139C22×C4—2511no—
140C2×C8—21no—
141C2×C8—21no—
142C2×C8—5024no—
143C2×C8—5021no—
144C2×C8—5021no—
145C4⋊C4—5021no—
146C4⋊C4—5021no—
147C4⋊C4—5021no—
148C4⋊C4—5021no—
149C4⋊C4—2511no—
150C4⋊C4C4×D25111yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—5021no—
153C22⋊C4—5021no—
154C22⋊C4—5021no—
155C22⋊C4—5021no—
156C42—5021no—
157C42—2511no—
158C42—2511no—
159C42—2511no—
160C42C22×D25111yescharacteristic
161C23—21no—
162C23—2511no—
163Q8—5021no—
164Q8—5021no—
165D4—21no—
166D4—21no—
167D4—10042no—
168C2×C4—21no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—5022no—
172C2×C4—5021no—
173C2×C4—5021no—
174C2×C4—5021no—
175C2×C4—5021no—
176C2×C4—5021no—
177C2×C4—5021no—
178C2×C4—2511no—
179C2×C4—2511no—
180C2×C4—2511no—
181C2×C4C2×C4×D25111yescharacteristic
182C2×C4D4×D25111yescharacteristic
183C2×C4D4×D25111yescharacteristic
184C8—22no—
185C8—41no—
186C8—10041no—
187C8—5022no—
188C22—41no—
189C22—41no—
190C22—41no—
191C22—5021no—
192C22—5021no—
193C22—2512no—
194C22C22⋊C4×D25111yescharacteristic
195C4—21no—
196C4—41no—
197C4—10041no—
198C4—10041no—
199C4—5021no—
200C4—5021no—
201C4—5021no—
202C4#2254872111yescharacteristic
203C4#2254872311yescharacteristic
204C4#2254873411yescharacteristic
205C4#2254873611yescharacteristic
206C2—81no—
207C2—5022no—
208C2#3063165211yescharacteristic
209C2#3063168011yescharacteristic
210C2#104×D25111yescharacteristic
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#1494
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. #30631743C2semidirect
3. C4×C8×D251C2semidirect
4. #30631419C2semidirect
5. #30631417C2semidirect
6. D4⋊(C251⋊C8)C2semidirect
7. D4⋊C8×C251C2semidirect
105. C251#1494semidirect
113. D4⋊C8D251semidirect

Maximal subgroups

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

subgroupindex
#306322192
#306317432
C4×C8×D2512
#306314192
#306314172
D4⋊(C251⋊C8)2
D4⋊C8×C2512
#1494251