Finite Group Databasebeta

← #44560651

Subgroups — #44560651

Order 32128.

382 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 121 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#30632164C211yesmaximal, characteristic, complemented
2#30632008C212yesmaximal, complemented
3#30631991C212yesmaximal, complemented
4#30631884C212yesmaximal, complemented
5#30631825C212yesmaximal, complemented
6#30631787C212yesmaximal, complemented
7C4×#16860798C212yesmaximal, complemented
8#30631748C211yesmaximal, characteristic, complemented
9#540×C251C211yesmaximal, characteristic
10C22×Dic502C2211yescharacteristic
11C2×#16860798C2212yes—
12C2×#16860798C2212yes—
13C4×Dic502C2212yes—
14C4×Dic502C2212yes—
15#22548680—22no—
16#22548674C2211yescharacteristic
17#22548671—22no—
18#22548648C2212yes—
19#22548646C2212yes—
20C4⋊(C251⋊C8)C2212yes—
21#22548638C2212yes—
22#22548638C2212yes—
23#22548636C2212yes—
24#22548636C2212yes—
25C22⋊(C251⋊C8)C2212yes—
26#22548626C2211yescharacteristic
27C4×C251⋊C8C2211yescharacteristic
28#127×C251C2211yescharacteristic
29#125×C251C2211yescharacteristic
30#123×C251—22no—
31#121×C251—22no—
32#121×C251C2212yes—
33C4×D4×C251C2212yes—
34#117×C251C2211yescharacteristic
35C2×Dic502—24no—
36C2×Dic502—21no—
37C2×Dic502C2312yes—
38C22×Dic251—21no—
39#16860798—24no—
40#16860798—24no—
41C2×C251⋊C8C2312yes—
42C2×C251⋊C8C2312yes—
43C4⋊Dic251C2312yes—
44Dic251⋊C4—22no—
45Dic251⋊C4—22no—
46C22⋊Dic251—21no—
47C4×Dic251—22no—
48C4×Dic251—22no—
49C4×Dic251—21no—
50C2×D4×C251—22no—
51C2×D4×C251—22no—
52C2×D4×C251C2312yes—
53C22×C4×C251—22no—
54C22×C4×C251C2311yescharacteristic
55C4⋊C4×C251—22no—
56C4⋊C4×C251D412yes—
57C4⋊C4×C251C2312yes—
58C22⋊C4×C251—22no—
59C22⋊C4×C251—22no—
60C22⋊C4×C251D412yes—
61C42×C251C2311yescharacteristic
62C42×C251C2311yescharacteristic
63Dic502—24no—
64Dic502—22no—
65Dic502#4114yes—
66C2×Dic251—24no—
67C2×Dic251—22no—
68C2×Dic251—22no—
69C251⋊C8—22no—
70C251⋊C8—22no—
71C23×C251—22no—
72C23×C251C2×D411yescharacteristic
73D4×C251—22no—
74D4×C251—22no—
75D4×C251—82no—
76D4×C251—82no—
77C2×C4×C251—22no—
78C2×C4×C251—22no—
79C2×C4×C251—82no—
80C2×C4×C251C2×D412yes—
81C2×C4×C251C2×D412yes—
82C2×C4×C251C2×D411yescharacteristic
83C2×C4×C251C2411yescharacteristic
84C22×C251—21no—
85C22×C251—22no—
86C22×C251—42no—
87C22×C251—42no—
88C22×C251—42no—
89C22×C251C22×D411yescharacteristic
90C4×C251—21no—
91C4×C251—22no—
92C4×C251—22no—
93C4×C251—42no—
94C4×C251C2×#4112yes—
95Dic251—24no—
96Dic251—42no—
97C2×C251—41no—
98C2×C251—82no—
99C2×C251#52511yescharacteristic
100C2×C251#57712yes—
101C251#312611yescharacteristic, complemented, Sylow
102#3126—2511nomaximal, Sylow
103#540D25111yescharacteristic
104#519—2511no—
105#482—2512no—
106#479—2512no—
107#460—2512no—
108#448—2512no—
109#440—2512no—
110C4×SD16—2512no—
111#433—2511no—
112C22×Q8—2511no—
113C2×SD16—2512no—
114C2×SD16—2512no—
115#127C2×D25111yescharacteristic
116#125C2×D25111yescharacteristic
117#123—22no—
118#121—22no—
119#121C2×D25112yes—
120C4×Q8—5022no—
121C4×Q8—2512no—
122C4×Q8—2512no—
123C4×D4C2×D25112yes—
124#117—5022no—
125#117—2511no—
126#117C2×D25111yescharacteristic
127#107—2512no—
128#106—2512no—
129C4⋊C8—2512no—
130#103—2512no—
131#103—2512no—
132#102—2512no—
133#102—2512no—
134C22⋊C8—2512no—
135#97—2511no—
136C4×C8—2511no—
137C2×Q8—5024no—
138C2×Q8—5021no—
139C2×Q8—2512no—
140C2×D4—22no—
141C2×D4—22no—
142C2×D4C22×D25112yes—
143C22×C4—22no—
144C22×C4—5021no—
145C22×C4C22×D25111yescharacteristic
146SD16—5024no—
147SD16—5024no—
148C2×C8—2512no—
149C2×C8—2512no—
150C4⋊C4—22no—
151C4⋊C4—5022no—
152C4⋊C4—5022no—
153C4⋊C4—2512no—
154C4⋊C4C22⋊D25112yes—
155C4⋊C4C22×D25112yes—
156C22⋊C4—22no—
157C22⋊C4—22no—
158C22⋊C4—5021no—
159C22⋊C4C22⋊D25112yes—
160C42—5022no—
161C42—5022no—
162C42—5021no—
163C42C22×D25111yescharacteristic
164C42C22×D25111yescharacteristic
165C23—22no—
166C23C2×C22⋊D25111yescharacteristic
167Q8—5024no—
168Q8—5022no—
169Q8—2514no—
170D4—22no—
171D4—22no—
172D4—82no—
173D4—82no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—82no—
177C2×C4—5022no—
178C2×C4—5024no—
179C2×C4—5022no—
180C2×C4C2×C22⋊D25112yes—
181C2×C4C2×C22⋊D25112yes—
182C2×C4C2×C22⋊D25111yescharacteristic
183C2×C4C23×D25111yescharacteristic
184C8—5022no—
185C8—5022no—
186C22—21no—
187C22—22no—
188C22—42no—
189C22—42no—
190C22—42no—
191C22C22×C22⋊D25111yescharacteristic
192C4—21no—
193C4—22no—
194C4—22no—
195C4—42no—
196C4—10042no—
197C4—5024no—
198C4#41×D25112yes—
199C2—41no—
200C2—82no—
201C2#3063219411yescharacteristic
202C2#3063249812yes—
subgroupG/H
centerC22C22×C22⋊D251
commutator, cosocleC2×C4×C251C24
FrattiniC2×C4C23×D251
Fitting, prime radical#540×C251C2
socleC22×C251C22×D4
hypercenter#540D251
hypocenterC251#3126
LCSG ▷ C2×C4×C251 ▷ C2×C251 ▷ C251
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #30632164C2semidirect
2. #30632008C2semidirect
3. #30631991C2semidirect
4. #30631884C2semidirect
5. #30631825C2semidirect
6. #30631787C2semidirect
7. C4×#16860798C2semidirect
8. #30631748C2semidirect
101. C251#3126semidirect

Maximal subgroups

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

subgroupindex
#306321642
#306320082
#306319912
#306318842
#306318252
#306317872
C4×#168607982
#306317482
#540×C2512
#3126251