Finite Group Databasebeta

← #44548677

Subgroups — #44548677

Order 32128.

264 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 93 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
1C2×#22548672C211yesmaximal, characteristic
2#30631740C211yesmaximal, characteristic, complemented
3#30631412C212yesmaximal, complemented
4#30631410C212yesmaximal
5#431×C251C211yesmaximal, characteristic, complemented
6C22×C4×D251C411yescharacteristic
7#22548672—21no—
8#22548672—21no—
9#22548672—21no—
10#22548672—21no—
11C2×Dic251⋊C4C411yescharacteristic
12C2×Dic251⋊C4C2211yescharacteristic
13C2×(C2×D251)⋊C4C411yescharacteristic
14C2×(C2×D251)⋊C4C2211yescharacteristic
15C2×C4×Dic251C411yescharacteristic
16C4⋊(C251⋊C8)—21no—
17C22⋊(C251⋊C8)C2212yes—
18C4×C251⋊C8—21no—
19C2×C42×C251C2211yescharacteristic
20C4⋊C8×C251—21no—
21C22⋊C8×C251C2212yes—
22C4×C8×C251—21no—
23C23×D251C2×C411yescharacteristic
24C22×Dic251C2×C411yescharacteristic
25C22×Dic251C2×C411yescharacteristic
26C22×Dic251C2×C411yescharacteristic
27C2×C4×D251—21no—
28C2×C4×D251—21no—
29C2×C4×D251—22no—
30C2×C4×D251C814yescomplemented
31C2×C251⋊C8—22no—
32Dic251⋊C4—21no—
33Dic251⋊C4—21no—
34Dic251⋊C4—21no—
35Dic251⋊C4—21no—
36(C2×D251)⋊C4—21no—
37(C2×D251)⋊C4—21no—
38(C2×D251)⋊C4—21no—
39(C2×D251)⋊C4—21no—
40C4×Dic251—21no—
41C4×Dic251—21no—
42C22×C4×C251C2×C411yescharacteristic
43C22×C4×C251C2×C411yescharacteristic
44C22×C4×C251C2311yescharacteristic
45C2×C8×C251—22no—
46C42×C251D411yescharacteristic
47C42×C251D411yescharacteristic
48C42×C251D411yescharacteristic
49C42×C251D411yescharacteristic
50C22×D251—21no—
51C22×D251—21no—
52C22×D251—41no—
53C22×D251—41no—
54C22×D251C2×C812yes—
55C2×Dic251—21no—
56C2×Dic251—21no—
57C2×Dic251—21no—
58C2×Dic251—21no—
59C2×Dic251—41no—
60C2×Dic251—41no—
61C2×Dic251C2×C812yes—
62C4×D251—24no—
63C4×D251—24no—
64C251⋊C8—42no—
65C23×C251C22×C411yescharacteristic
66C2×C4×C251—41no—
67C2×C4×C251—41no—
68C2×C4×C251C22⋊C411yescharacteristic
69C2×C4×C251C22⋊C411yescharacteristic
70C2×C4×C251C22⋊C411yescharacteristic
71C2×C4×C251C22⋊C411yescharacteristic
72C2×C4×C251C2×C812yes—
73C2×C4×C251M1612yes—
74C2×C4×C251C2×D411yescharacteristic
75C2×C4×C251C2×D411yescharacteristic
76C8×C251—42no—
77C22×C251—21no—
78C22×C251—21no—
79C22×C251C2×C22⋊C411yescharacteristic
80C22×C251C22×C811yescharacteristic
81C22×C251C2×M1611yescharacteristic
82C2×D251—22no—
83C2×D251—42no—
84C2×D251—41no—
85C2×D251—41no—
86C2×D251—42no—
87C4×C251—21no—
88C4×C251—21no—
89C4×C251—21no—
90C4×C251—21no—
91C4×C251C22⋊C812yes—
92C4×C251C22⋊C812yes—
93Dic251—22no—
94Dic251—41no—
95Dic251—41no—
96C2×C251—21no—
97C2×C251—21no—
98C2×C251C2×C22⋊C811yescharacteristic
99C2×C251#41011yescharacteristic
100C2×C251#41311yescharacteristic
101D251—42no—
102C251#145811yescharacteristic, complemented, Sylow
103#1458—2511nomaximal, Sylow
104C2×#117—2511no—
105#431—2511no—
106#431D25111yescharacteristic, complemented
107#324—2512no—
108#323—2512no—
109C23×C4—2511no—
110#117—5021no—
111#117—5021no—
112#117—5021no—
113#117—5021no—
114C2×C4⋊C4—2511no—
115C2×C4⋊C4—2511no—
116C2×C22⋊C4—2511no—
117C2×C22⋊C4—2511no—
118C2×C42—2511no—
119C2×C42C2×D25111yescharacteristic
120C4⋊C8—21no—
121C4⋊C8—5021no—
122C22⋊C8—2512no—
123C22⋊C8C2×D25112yes—
124C4×C8—21no—
125C4×C8—5021no—
126C24—2511no—
127C22×C4—5021no—
128C22×C4—5021no—
129C22×C4—5022no—
130C22×C4—2511no—
131C22×C4—2511no—
132C22×C4—2511no—
133C22×C4—2514no—
134C22×C4C4×D25111yescharacteristic
135C22×C4C4×D25111yescharacteristic
136C22×C4C22×D25111yescharacteristic
137C2×C8—22no—
138C2×C8—5022no—
139C4⋊C4—5021no—
140C4⋊C4—5021no—
141C4⋊C4—5021no—
142C4⋊C4—5021no—
143C22⋊C4—5021no—
144C22⋊C4—5021no—
145C22⋊C4—5021no—
146C22⋊C4—5021no—
147C42—5021no—
148C42—5021no—
149C42C22⋊D25111yescharacteristic
150C42C22⋊D25111yescharacteristic
151C42D100411yescharacteristic
152C42D100411yescharacteristic
153C23—10041no—
154C23—10041no—
155C23—5021no—
156C23—5021no—
157C23—2512no—
158C23C2×C4×D25111yescharacteristic
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—10041no—
162C2×C4—10041no—
163C2×C4—5021no—
164C2×C4—5021no—
165C2×C4—5021no—
166C2×C4—5021no—
167C2×C4—5024no—
168C2×C4—5024no—
169C2×C4—2512no—
170C2×C4(C2×D251)⋊C411yescharacteristic
171C2×C4(C2×D251)⋊C411yescharacteristic
172C2×C4(C2×D251)⋊C411yescharacteristic
173C2×C4(C2×D251)⋊C411yescharacteristic
174C2×C4C8×D25112yes—
175C2×C4#1686079312yes—
176C2×C4C2×C22⋊D25111yescharacteristic
177C2×C4C2×D100411yescharacteristic
178C8—42no—
179C8—10042no—
180C22—21no—
181C22—21no—
182C22—10042no—
183C22—10042no—
184C22—10041no—
185C22—10041no—
186C22—5022no—
187C22C2×(C2×D251)⋊C411yescharacteristic
188C22C2×C8×D25111yescharacteristic
189C22C2×#1686079311yescharacteristic
190C4—21no—
191C4—21no—
192C4—21no—
193C4—21no—
194C4—10041no—
195C4—10041no—
196C4—5022no—
197C4(C2×D251)⋊C812yes—
198C4(C2×D251)⋊C812yes—
199C2—21no—
200C2—21no—
201C2—10042no—
202C2C2×(C2×D251)⋊C811yescharacteristic
203C2#3063166011yescharacteristic
204C2#3063166911yescharacteristic
subgroupG/H
centerC2×C4(C2×D251)⋊C4
commutatorC22×C251C22×C8
FrattiniC22×C4C22×D251
Fitting#431×C251C2
socleC22×C251C2×C22⋊C4
prime radicalC23×D251C2×C4
cosocleC22×C4×C251C23
hypercenter#431D251
hypocenterC251#1458
LCSG ▷ C22×C251 ▷ C2×C251 ▷ C251
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
2. #30631740C2semidirect
3. #30631412C2semidirect
5. #431×C251C2semidirect
30. C2×C4×D251C8semidirect
102. C251#1458semidirect
106. #431D251semidirect

Maximal subgroups

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

subgroupindex
C2×#225486722
#306317402
#306314122
#306314102
#431×C2512
#1458251