Finite Group Databasebeta

← #44549439

Subgroups — #44549439

Order 32128.

236 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 57 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#30632394C211yesmaximal, characteristic, complemented
2#30632060C211yesmaximal, characteristic, complemented
3#30631888C211yesmaximal, characteristic, complemented
4#30631882C211yesmaximal, characteristic
5#30631435C211yesmaximal, characteristic, complemented
6#30631419C211yesmaximal, characteristic, complemented
7D4⋊C8×C251C211yesmaximal, characteristic, complemented
8C2×#16860799—22no—
9C2×#16860799—21no—
10C2×#16860795—21no—
11#22548715C2211yescharacteristic
12#22548712C2211yescharacteristic
13#22548706—21no—
14#22548694—21no—
15#22548692—22no—
16C4×Dic502C2211yescharacteristic
17D4×Dic251—21no—
18C2×C4⋊Dic251—21no—
19C4⋊(C251⋊C8)C2211yescharacteristic
20#22548637—21no—
21#22548635—21no—
22C4×D4×C251C2211yescharacteristic
23C4⋊C8×C251C2211yescharacteristic
24C4×C8×C251C2211yescharacteristic
25C2×Dic502D411yescharacteristic
26C2×Dic502D412yes—
27C2×D1004—21no—
28C2×D1004—21no—
29C2×D1004—21no—
30C22×Dic251—22no—
31#16860799—44no—
32#16860799—42no—
33#16860795—42no—
34C2×C251⋊C8—21no—
35C4⋊Dic251—22no—
36C4⋊Dic251—21no—
37C4⋊Dic251—21no—
38C4⋊Dic251D411yescharacteristic
39Dic251⋊C4—22no—
40Dic251⋊C4—21no—
41C22⋊Dic251—22no—
42C4×Dic251—21no—
43C2×D4×C251D411yescharacteristic
44C22×C4×C251—21no—
45C2×C8×C251—21no—
46C2×C8×C251—21no—
47C4⋊C4×C251D411yescharacteristic
48C22⋊C4×C251—21no—
49C42×C251C2311yescharacteristic
50C22×D251—41no—
51Dic502—21no—
52Dic502—21no—
53Dic502—42no—
54D1004—42no—
55D1004—41no—
56D1004—41no—
57D1004—41no—
58D1004—41no—
59C2×Dic251—21no—
60C2×Dic251—21no—
61C2×Dic251—22no—
62C2×Dic251—82no—
63C251⋊C8—41no—
64C23×C251—21no—
65D4×C251—21no—
66D4×C251SD1612yescomplemented
67C2×C4×C251—21no—
68C2×C4×C251—41no—
69C2×C4×C251—41no—
70C2×C4×C251C2×D411yescharacteristic
71C2×C4×C251C2×D411yescharacteristic
72C2×C4×C251C2×D411yescharacteristic
73C8×C251—22no—
74C8×C251—41no—
75C22×C251—22no—
76C22×C251—41no—
77C22×C251—41no—
78C22×C251#12011yescharacteristic
79C2×D251—81no—
80C2×D251—81no—
81C2×D251—81no—
82C4×C251—21no—
83C4×C251—41no—
84C4×C251C2×SD1611yescharacteristic
85C4×C251#13511yescharacteristic
86C4×C251AGL(1,ℤ/8)11yescharacteristic
87C4×C251#13711yescharacteristic
88Dic251—41no—
89Dic251—41no—
90Dic251—42no—
91C2×C251—42no—
92C2×C251#44811yescharacteristic
93C2×C251#44911yescharacteristic
94C2×C251#45311yescharacteristic
95D251—161no—
96C251#162211yescharacteristic, complemented, Sylow
97#1622—2511nomaximal, Sylow
98#554—2511no—
99#492—2511no—
100#460—2511no—
101#459—2511no—
102#333—2511no—
103Q8⋊C8—2511no—
104D4⋊C8D25111yescharacteristic, complemented
105C2×SD16—5021no—
106C2×SD16—5022no—
107C2×D8—5021no—
108C4⋊Q8—2511no—
109#127—2511no—
110#125—5021no—
111C22⋊Q8—5022no—
112C22⋊Q8—5021no—
113C4×Q8—2511no—
114C4×D4—5021no—
115C4×D4C2×D25111yescharacteristic
116C2×C4⋊C4—5021no—
117C4⋊C8—2511no—
118C4⋊C8C2×D25111yescharacteristic
119#102—5021no—
120#102—5021no—
121C4×C8C2×D25111yescharacteristic
122C2×Q8—2512no—
123C2×Q8—2511no—
124C2×D4—5021no—
125C2×D4—5021no—
126C2×D4—5021no—
127C2×D4D100411yescharacteristic
128C22×C4—21no—
129C22×C4—5022no—
130SD16—10044no—
131SD16—10042no—
132D8—10042no—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—5021no—
136C4⋊C4—5022no—
137C4⋊C4—5022no—
138C4⋊C4—5021no—
139C4⋊C4—5021no—
140C4⋊C4—5021no—
141C4⋊C4—2511no—
142C4⋊C4D100411yescharacteristic
143C22⋊C4—21no—
144C22⋊C4—5022no—
145C42—5021no—
146C42C22×D25111yescharacteristic
147C23—21no—
148C23—10041no—
149Q8—10042no—
150Q8—5021no—
151Q8—5021no—
152D4—21no—
153D4—10042no—
154D4—10041no—
155D4—10041no—
156D4—10041no—
157D4—10041no—
158D4#1686079912yescomplemented
159C2×C4—21no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—20082no—
163C2×C4—5021no—
164C2×C4—5021no—
165C2×C4—5022no—
166C2×C4D4×D25111yescharacteristic
167C2×C4D4×D25111yescharacteristic
168C2×C4C2×D100411yescharacteristic
169C8—22no—
170C8—41no—
171C8—10041no—
172C22—22no—
173C22—41no—
174C22—41no—
175C22—20081no—
176C22—20081no—
177C22—20081no—
178C22#2254868511yescharacteristic
179C4—21no—
180C4—41no—
181C4—10041no—
182C4—10041no—
183C4—10042no—
184C4C2×#1686079911yescharacteristic
185C4#2254873611yescharacteristic
186C4#2254873911yescharacteristic
187C4#2254874811yescharacteristic
188C2—42no—
189C2—40161no—
190C2#3063182811yescharacteristic
191C2#3063183311yescharacteristic
192C2#3063185611yescharacteristic
subgroupG/H
centerC22#22548685
commutator, cosocleC42×C251C23
FrattiniC42C22×D251
FittingD4⋊C8×C251C2
socleC22×C251#120
prime radical#30631882C2
hypercenterD4⋊C8D251
hypocenterC251#1622
LCSG ▷ C42×C251 ▷ C22×C251 ▷ C251
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
1. #30632394C2semidirect
2. #30632060C2semidirect
3. #30631888C2semidirect
5. #30631435C2semidirect
6. #30631419C2semidirect
7. D4⋊C8×C251C2semidirect
66. D4×C251SD16semidirect
96. C251#1622semidirect
104. D4⋊C8D251semidirect
158. D4#16860799semidirect

Maximal subgroups

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

subgroupindex
#306323942
#306320602
#306318882
#306318822
#306314352
#306314192
D4⋊C8×C2512
#1622251