Finite Group Databasebeta

← #44549405

Subgroups — #44549405

Order 32128.

202 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 51 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#30632316C211yesmaximal, characteristic
2#30632022C211yesmaximal, characteristic
3#30631625C211yesmaximal, characteristic
4#30631425C211yesmaximal, characteristic
5#30631424C211yesmaximal, characteristic
6#30631412C211yesmaximal, characteristic
7#484×C251C211yesmaximal, characteristic
8#22548714—21no—
9#22548713—21no—
10#22548705—21no—
11#22548705—21no—
12#22548694C2211yescharacteristic
13#22548692—21no—
14#22548671—21no—
15C2×Dic251⋊C4C2211yescharacteristic
16#22548648—21no—
17#22548638—21no—
18C22⋊(C251⋊C8)C2211yescharacteristic
19C251⋊#95—21no—
20C251⋊#95—21no—
21C251⋊#95C2211yescharacteristic
22C22⋊Q8×C251C2211yescharacteristic
23C2×C4⋊C4×C251C2211yescharacteristic
24#107×C251—21no—
25#103×C251—21no—
26C22⋊C8×C251C2211yescharacteristic
27C2×Dic502—21no—
28C2×Dic502D411yescharacteristic
29C22×Dic251—21no—
30C22×Dic251D411yescharacteristic
31C22×Dic251D411yescharacteristic
32C2×C251⋊C8—21no—
33C4⋊Dic251—21no—
34C4⋊Dic251D411yescharacteristic
35Dic251⋊C4—21no—
36Dic251⋊C4—21no—
37Dic251⋊C4—21no—
38Dic251⋊C4—21no—
39Dic251⋊C4—21no—
40Dic251⋊C4—21no—
41Dic251⋊C4—21no—
42C22⋊Dic251—21no—
43C4×Dic251—21no—
44C4×Dic251—21no—
45C2×Q8×C251D411yescharacteristic
46C22×C4×C251—21no—
47C22×C4×C251C2311yescharacteristic
48C2×C8×C251—21no—
49C4⋊C4×C251—21no—
50C4⋊C4×C251—21no—
51C4⋊C4×C251—21no—
52C4⋊C4×C251D411yescharacteristic
53C22⋊C4×C251—21no—
54Dic502—41no—
55Dic502—81no—
56C2×Dic251—21no—
57C2×Dic251—21no—
58C2×Dic251—21no—
59C2×Dic251—21no—
60C2×Dic251—21no—
61C2×Dic251—41no—
62C2×Dic251—41no—
63C2×Dic251—41no—
64C2×Dic251—41no—
65C2×Dic251Q1612yes—
66C251⋊C8—41no—
67C23×C251C2×D411yescharacteristic
68Q8×C251—41no—
69C2×C4×C251—21no—
70C2×C4×C251—21no—
71C2×C4×C251—41no—
72C2×C4×C251—42no—
73C2×C4×C251—41no—
74C2×C4×C251C2×D411yescharacteristic
75C2×C4×C251C2×D411yescharacteristic
76C8×C251—41no—
77C22×C251—21no—
78C22×C251—21no—
79C22×C251#12011yescharacteristic
80C22×C251C2×Q1611yescharacteristic
81C22×C251#13711yescharacteristic
82C4×C251—21no—
83C4×C251—21no—
84C4×C251—41no—
85C4×C251—41no—
86C4×C251—81no—
87Dic251—22no—
88Dic251—41no—
89Dic251—41no—
90Dic251—41no—
91Dic251—81no—
92C2×C251—21no—
93C2×C251—21no—
94C2×C251#45111yescharacteristic
95C2×C251#45411yescharacteristic
96C2×C251#45811yescharacteristic
97C251#161711yescharacteristic, complemented, Sylow
98#1617—2511nomaximal, Sylow
99#544—2511no—
100#484—2511no—
101#484D25111yescharacteristic
102#400—2511no—
103#328—2511no—
104#328—2511no—
105#324—2511no—
106C4⋊Q8—5021no—
107C4⋊Q8—5021no—
108#125—5021no—
109#125—5021no—
110C22⋊Q8—5021no—
111C22⋊Q8—2511no—
112C22⋊Q8C2×D25111yescharacteristic
113#117—5021no—
114C2×C4⋊C4—2511no—
115C2×C4⋊C4C2×D25111yescharacteristic
116#107—21no—
117#107—5021no—
118#103—21no—
119#103—5021no—
120C22⋊C8—2511no—
121C22⋊C8C2×D25111yescharacteristic
122#95—5021no—
123#95—5021no—
124#95—2511no—
125C2×Q8—5021no—
126C2×Q8—2511no—
127C2×Q8C22⋊D25111yescharacteristic
128C22×C4—21no—
129C22×C4—5021no—
130C22×C4—2511no—
131C22×C4—2511no—
132C22×C4C22×D25111yescharacteristic
133C2×C8—21no—
134C2×C8—5021no—
135C4⋊C4—21no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—5021no—
139C4⋊C4—5021no—
140C4⋊C4—5021no—
141C4⋊C4—5021no—
142C4⋊C4—5021no—
143C4⋊C4—5021no—
144C4⋊C4—5021no—
145C4⋊C4—5021no—
146C4⋊C4—2511no—
147C4⋊C4C22⋊D25111yescharacteristic
148C22⋊C4—21no—
149C22⋊C4—5021no—
150C42—5021no—
151C42—5021no—
152C23D4×D25111yescharacteristic
153Q8—41no—
154Q8—20081no—
155Q8—10041no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—41no—
159C2×C4—42no—
160C2×C4—41no—
161C2×C4—10041no—
162C2×C4—10041no—
163C2×C4—10041no—
164C2×C4—10041no—
165C2×C4—5021no—
166C2×C4—5021no—
167C2×C4—5021no—
168C2×C4—5021no—
169C2×C4—5021no—
170C2×C4—2512no—
171C2×C4D4×D25111yescharacteristic
172C2×C4C2×C22⋊D25111yescharacteristic
173C8—41no—
174C8—10041no—
175C22—21no—
176C22—21no—
177C22#2254868311yescharacteristic
178C22Q16×D25111yescharacteristic
179C22#2254874711yescharacteristic
180C4—21no—
181C4—21no—
182C4—41no—
183C4—41no—
184C4—81no—
185C4—20081no—
186C4—10041no—
187C4—10041no—
188C4—10041no—
189C4—5022no—
190C2—21no—
191C2—21no—
192C2#3063184111yescharacteristic
193C2#3063185811yescharacteristic
194C2#3063187611yescharacteristic
subgroupG/H
centerC22#22548683
commutator, cosocleC22×C4×C251C23
FrattiniC22×C4C22×D251
Fitting#484×C251C2
socleC22×C251#120
prime radicalC23×C251C2×D4
hypercenter#484D251
hypocenterC251#1617
LCSG ▷ C22×C4×C251 ▷ C22×C251 ▷ C251
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
97. C251#1617semidirect

Maximal subgroups

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

subgroupindex
#306323162
#306320222
#306316252
#306314252
#306314242
#306314122
#484×C2512
#1617251