Finite Group Databasebeta

← #44550757

Subgroups — #44550757

Order 32128.

324 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 83 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×#22548715C211yesmaximal, characteristic
2#30632164C211yesmaximal, characteristic
3#30631697C211yesmaximal, characteristic
4#30631695C211yesmaximal, characteristic
5C2×#22548633C211yesmaximal, characteristic
6#30631447C211yesmaximal, characteristic
7#339×C251C211yesmaximal, characteristic
8C22×Dic502C2211yescharacteristic
9C22×Dic502C2211yescharacteristic
10C2×#16860794C2211yescharacteristic
11#22548715—22no—
12#22548715C414yescomplemented
13C4×Dic502—22no—
14#22548680—22no—
15#22548674C2211yescharacteristic
16#22548671—22no—
17C2×C4⋊Dic251—22no—
18#22548640—22no—
19#22548638—22no—
20#22548633—22no—
21C2×M16×C251C2211yescharacteristic
22#117×C251C2211yescharacteristic
23C2×C42×C251C2211yescharacteristic
24C2×Dic502—21no—
25C2×Dic502—21no—
26C2×Dic502—21no—
27C2×Dic502—21no—
28C2×Dic502—21no—
29C2×Dic502—21no—
30C2×Dic502—21no—
31C2×Dic502—21no—
32C2×Dic502—21no—
33C2×Dic502C2×C412yes—
34C2×Dic502C2×C412yes—
35C2×Dic502D412yes—
36C22×Dic251—21no—
37C22×Dic251D412yes—
38#16860794—21no—
39#16860794—21no—
40C2×C251⋊C8—21no—
41C4⋊Dic251—28no—
42C4⋊Dic251D412yes—
43Dic251⋊C4—24no—
44C22⋊Dic251—21no—
45C4×Dic251—24no—
46C4×Dic251—21no—
47C22×C4×C251—21no—
48C22×C4×C251C2311yescharacteristic
49M16×C251—21no—
50M16×C251—21no—
51C2×C8×C251—21no—
52C4⋊C4×C251D412yes—
53C22⋊C4×C251—21no—
54C42×C251—21no—
55C42×C251—21no—
56C42×C251C2×C412yes—
57Dic502—22no—
58Dic502—22no—
59Dic502—22no—
60Dic502—22no—
61Dic502—22no—
62Dic502—22no—
63Dic502—41no—
64Dic502—41no—
65C2×Dic251—22no—
66C2×Dic251—22no—
67C2×Dic251—22no—
68C2×Dic251—22no—
69C2×Dic251—41no—
70C2×Dic251—41no—
71C2×Dic251C22⋊C414yes—
72C251⋊C8—41no—
73C23×C251C2×D411yescharacteristic
74C2×C4×C251—24no—
75C2×C4×C251—22no—
76C2×C4×C251—22no—
77C2×C4×C251C22×C411yescharacteristic
78C2×C4×C251C2×D411yescharacteristic
79C2×C4×C251C2×D411yescharacteristic
80C2×C4×C251C2×D411yescharacteristic
81C2×C4×C251#4111yescharacteristic
82C2×C4×C251#4111yescharacteristic
83C8×C251—41no—
84C22×C251—22no—
85C22×C251C2×C22⋊C411yescharacteristic
86C22×C251#12011yescharacteristic
87C22×C251#12311yescharacteristic
88C4×C251—24no—
89C4×C251—42no—
90C4×C251C4×D411yescharacteristic
91C4×C251C4×D411yescharacteristic
92C4×C251#12111yescharacteristic
93C4×C251#12111yescharacteristic
94Dic251—24no—
95Dic251—42no—
96Dic251—42no—
97C2×C251—21no—
98C2×C251—21no—
99C2×C251#38611yescharacteristic
100C2×C251#45612yes—
101C251#188611yescharacteristic, complemented, Sylow
102#1886—2511nomaximal, Sylow
103C2×C4⋊Q8—2511no—
104#519—2511no—
105#419—2511no—
106#419—2511no—
107C2×#101—2511no—
108#339—2511no—
109#339D25111yescharacteristic
110C22×Q8—2511no—
111C22×Q8—2511no—
112C2×M16—2511no—
113C2×M16C2×D25111yescharacteristic
114C4⋊Q8—5022no—
115C4⋊Q8—2514no—
116C4×Q8—5022no—
117C4×Q8—5022no—
118#117—5022no—
119#117—2511no—
120#117C2×D25111yescharacteristic
121C2×C4⋊C4—5022no—
122C2×C42C2×D25111yescharacteristic
123#103—5022no—
124#103—5022no—
125#101—5022no—
126C2×Q8—5021no—
127C2×Q8—5021no—
128C2×Q8—5021no—
129C2×Q8—5021no—
130C2×Q8—5021no—
131C2×Q8—5021no—
132C2×Q8—5021no—
133C2×Q8—5021no—
134C2×Q8—5021no—
135C2×Q8—2512no—
136C2×Q8—2512no—
137C2×Q8—2512no—
138C22×C4—21no—
139C22×C4—5021no—
140C22×C4—2512no—
141C22×C4C22×D25111yescharacteristic
142M16—21no—
143M16—21no—
144M16—5021no—
145M16—5021no—
146C2×C8—21no—
147C2×C8—5021no—
148C4⋊C4—5024no—
149C4⋊C4—5028no—
150C4⋊C4—2512no—
151C4⋊C4D100412yes—
152C22⋊C4—21no—
153C22⋊C4—5021no—
154C42—21no—
155C42—21no—
156C42—5024no—
157C42—5021no—
158C42C4×D25112yes—
159C23D4×D25111yescharacteristic
160Q8—10041no—
161Q8—10041no—
162Q8—5022no—
163Q8—5022no—
164Q8—5022no—
165Q8—5022no—
166Q8—5022no—
167Q8—5022no—
168C2×C4—24no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—10041no—
172C2×C4—10041no—
173C2×C4—5022no—
174C2×C4—5022no—
175C2×C4—5022no—
176C2×C4—5022no—
177C2×C4—2514no—
178C2×C4C2×C4×D25111yescharacteristic
179C2×C4D4×D25111yescharacteristic
180C2×C4D4×D25111yescharacteristic
181C2×C4C2×D100411yescharacteristic
182C2×C4#1686081011yescharacteristic
183C2×C4#1686081111yescharacteristic
184C8—41no—
185C8—10041no—
186C22—22no—
187C22C22⋊C4×D25111yescharacteristic
188C22#2254868511yescharacteristic
189C22#2254870011yescharacteristic
190C4—24no—
191C4—42no—
192C4—10042no—
193C4—10042no—
194C4—5024no—
195C4#2254867711yescharacteristic
196C4C4×D100411yescharacteristic
197C4#2254868811yescharacteristic
198C4#2254869011yescharacteristic
199C2—21no—
200C2—21no—
201C2#3063156511yescharacteristic
202C2#3063187112yes—
subgroupG/H
centerC22#22548685
commutatorC2×C4×C251C22×C4
FrattiniC22×C4C22×D251
Fitting#339×C251C2
socleC22×C251#120
prime radicalC23×C251C2×D4
cosocleC22×C4×C251C23
hypercenter#339D251
hypocenterC251#1886
LCSG ▷ C2×C4×C251 ▷ C2×C251 ▷ C251
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
12. #22548715C4semidirect
101. C251#1886semidirect

Maximal subgroups

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

subgroupindex
C2×#225487152
#306321642
#306316972
#306316952
C2×#225486332
#306314472
#339×C2512
#1886251