Finite Group Databasebeta

← #27170281

Subgroups — #27170281

Order 12928.

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

normal subgroups only

This group has 234 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#20265831C211yesmaximal, characteristic
2#20265527C211yesmaximal, characteristic, complemented
3#20265464C211yesmaximal, characteristic, complemented
4#20264924C211yesmaximal, characteristic, complemented
5D4⋊#11717579C211yesmaximal, characteristic, complemented
6#20264904C211yesmaximal, characteristic, complemented
7#476×C101C211yesmaximal, characteristic, complemented
8C2×#13108073—21no—
9#15692255C2211yescharacteristic
10#15692239—22no—
11#15692235—21no—
12#15692229—21no—
13C4×D404C2211yescharacteristic
14C2×C4⋊Dic101—21no—
15#15692186—21no—
16C4⋊#11717579C2211yescharacteristic
17#15692179—22no—
18#15692175—21no—
19C4×#11717579C2211yescharacteristic
20C4⋊Q8×C101C2211yescharacteristic
21C4×D4×C101C2211yescharacteristic
22#106×C101—21no—
23C4⋊C8×C101C2211yescharacteristic
24#102×C101—21no—
25#13108073—42no—
26#13108073—42no—
27C2×Dic202—21no—
28C2×D404D411yescharacteristic
29C2×C22⋊D101—22no—
30C22×Dic101—22no—
31C2×C4×D101—21no—
32C2×#11717579—21no—
33C2×#11717579—21no—
34C4⋊Dic101—22no—
35C4⋊Dic101—21no—
36C4⋊Dic101D412yes—
37C4⋊Dic101D411yescharacteristic
38#13108051—22no—
39#13108051—21no—
40C2×Q8×C101—21no—
41C2×D4×C101D411yescharacteristic
42C22×C4×C101—21no—
43C2×C8×C101—21no—
44C4⋊C4×C101—21no—
45C4⋊C4×C101—21no—
46C4⋊C4×C101D411yescharacteristic
47C22⋊C4×C101—21no—
48C42×C101C2311yescharacteristic
49C23×C101—21no—
50C22×D101—21no—
51Q8×C101—42no—
52D4×C101—21no—
53D4×C101SD1612yes—
54C2×C4×C101—21no—
55C2×C4×C101—41no—
56C2×C4×C101—41no—
57C2×C4×C101—41no—
58C2×C4×C101C2×D411yescharacteristic
59C2×C4×C101C2×D411yescharacteristic
60C2×C4×C101C2×D411yescharacteristic
61C22⋊D101—44no—
62C2×Dic101—21no—
63C2×Dic101—22no—
64C2×Dic101—44no—
65D404—21no—
66D404—21no—
67C4×D101—41no—
68C4×D101—41no—
69Dic202—41no—
70Dic202—41no—
71C8×C101—41no—
72#11717579—41no—
73#11717579—41no—
74C22×C101—22no—
75C22×C101—41no—
76C22×C101—41no—
77C22×C101#12011yescharacteristic
78C2×D101—41no—
79C2×D101—41no—
80C2×D101—41no—
81C4×C101—21no—
82C4×C101—41no—
83C4×C101—81no—
84C4×C101C2×SD1611yescharacteristic
85C4×C101#13511yescharacteristic
86C4×C101AGL(1,ℤ/8)11yescharacteristic
87C4×C101#13711yescharacteristic
88Dic101—42no—
89Dic101—41no—
90C2×C101—42no—
91C2×C101#45011yescharacteristic
92C2×C101#45211yescharacteristic
93C2×C101#45411yescharacteristic
94D101—81no—
95#1635—1011nomaximal, Sylow
96C101#163511yescharacteristic, complemented, Sylow
97#547—1011no—
98#487—1011no—
99#476—1011no—
100#476D10111yescharacteristic, complemented
101#332—1011no—
102D4⋊C8—1011no—
103D4⋊C8—1011no—
104C2×#41—2021no—
105C4⋊Q8—1011no—
106C4⋊Q8C2×D10111yescharacteristic
107#123—2022no—
108C22⋊Q8—2021no—
109#121—2021no—
110C4×D4—1011no—
111C4×D4C2×D10111yescharacteristic
112C2×C4⋊C4—2021no—
113#106—21no—
114#106—2021no—
115C4⋊C8—1011no—
116C4⋊C8C2×D10111yescharacteristic
117#103—2022no—
118#102—21no—
119#102—2021no—
120C4×C8—1011no—
121#41—4042no—
122#41—4042no—
123C2×Q8—21no—
124C2×Q8—2021no—
125C2×D4—1011no—
126C2×D4—2022no—
127C2×D4C22⋊D10111yescharacteristic
128C22×C4—21no—
129C22×C4—2022no—
130C22×C4—2021no—
131C2×C8—21no—
132C2×C8—2021no—
133C2×C8—2021no—
134C4⋊C4—21no—
135C4⋊C4—21no—
136C4⋊C4—1012no—
137C4⋊C4—1011no—
138C4⋊C4—2022no—
139C4⋊C4—2021no—
140C4⋊C4C22⋊D10111yescharacteristic
141C22⋊C4—21no—
142C22⋊C4—2022no—
143C22⋊C4—2021no—
144C42C22×D10111yescharacteristic
145C23—21no—
146C23—2021no—
147Q8—42no—
148Q8—4041no—
149Q8—4041no—
150D4—21no—
151D4—4044no—
152D4—2021no—
153D4—2021no—
154D4#1310806112yes—
155C2×C4—21no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—4044no—
160C2×C4—4041no—
161C2×C4—4041no—
162C2×C4—2021no—
163C2×C4—2022no—
164C2×C4D4×D10111yescharacteristic
165C2×C4D4×D10111yescharacteristic
166C2×C4C2×C22⋊D10111yescharacteristic
167C8—41no—
168C8—4041no—
169C8—4041no—
170C22—22no—
171C22—41no—
172C22—41no—
173C22—4041no—
174C22—4041no—
175C22—4041no—
176C22#1569222311yescharacteristic
177C4—21no—
178C4—41no—
179C4—81no—
180C4—4041no—
181C4—4042no—
182C4C2×#1310806111yescharacteristic
183C4#1569227611yescharacteristic
184C4#1569228011yescharacteristic
185C4#1569228411yescharacteristic
186C2—42no—
187C2—8081no—
188C2#2026532711yescharacteristic
189C2#2026533611yescharacteristic
190C2#2026534811yescharacteristic
subgroupG/H
centerC22#15692223
commutator, cosocleC42×C101C23
FrattiniC42C22×D101
Fitting#476×C101C2
socleC22×C101#120
prime radical#20265831C2
hypercenter#476D101
hypocenterC101#1635
LCSG ▷ C42×C101 ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
2. #20265527C2semidirect
3. #20265464C2semidirect
4. #20264924C2semidirect
5. D4⋊#11717579C2semidirect
6. #20264904C2semidirect
7. #476×C101C2semidirect
96. C101#1635semidirect
100. #476D101semidirect

Maximal subgroups

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

subgroupindex
#202658312
#202655272
#202654642
#202649242
D4⋊#117175792
#202649042
#476×C1012
#1635101