Finite Group Databasebeta

← #27186650

Subgroups — #27186650

Order 12928.

216 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 68 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#20266180C211yesmaximal, characteristic
2C2×#15692322C211yesmaximal, characteristic
3#20266037C212yesmaximal, complemented
4#20266036C212yesmaximal, complemented
5#20265729C211yesmaximal, characteristic
6C2×#13108083—21no—
7C22×#11717581—21no—
8#15692322—21no—
9#15692322C2212yes—
10#15692322C2212yes—
11C4⋊#11717581—21no—
12#15692254C2211yescharacteristic
13#15692253C2211yescharacteristic
14#15692245—21no—
15#15692234C411yescharacteristic
16#15692232—21no—
17Q8×Dic101C411yescharacteristic
18#15692220—21no—
19#15692220C411yescharacteristic
20#15692211—21no—
21C2×C4×Dic101C2211yescharacteristic
22C22⋊Q8×C101C411yescharacteristic
23#13108083—42no—
24C2×#11717581—22no—
25C2×#11717581—22no—
26C2×#11717581—42no—
27C2×Dic202—21no—
28C2×Dic202C2×C411yescharacteristic
29C22×Dic101D411yescharacteristic
30C22×Dic101D411yescharacteristic
31C4⋊Dic101—21no—
32C4⋊Dic101C2×C411yescharacteristic
33#13108053—21no—
34#13108053—21no—
35#13108053—21no—
36#13108053—21no—
37#13108053—21no—
38C22⋊Dic101—21no—
39C4×Dic101—21no—
40C4×Dic101—21no—
41C4×Dic101C2×C411yescharacteristic
42C4×Dic101D411yescharacteristic
43C4×Dic101D411yescharacteristic
44C4×Dic101C2311yescharacteristic
45C2×Q8×C101C2×C411yescharacteristic
46C22×C4×C101C2×C411yescharacteristic
47C4⋊C4×C101—21no—
48C4⋊C4×C101C2×C411yescharacteristic
49C22⋊C4×C101—21no—
50C23×C101C22⋊C411yescharacteristic
51Q8×C101—41no—
52C2×C4×C101—21no—
53C2×C4×C101—21no—
54C2×C4×C101—41no—
55C2×C4×C101C22⋊C411yescharacteristic
56C2×C4×C101C22×C411yescharacteristic
57C2×Dic101—21no—
58C2×Dic101—21no—
59C2×Dic101—21no—
60C2×Dic101—21no—
61C2×Dic101C22⋊C411yescharacteristic
62C2×Dic101C22⋊C411yescharacteristic
63C2×Dic101SD1612yes—
64C2×Dic101Q1612yes—
65C2×Dic101C2×D411yescharacteristic
66C2×Dic101C2×D411yescharacteristic
67Dic202—41no—
68Dic202—41no—
69Dic202—41no—
70#11717581—42no—
71#11717581—42no—
72C22×C101—21no—
73C22×C101—21no—
74C22×C101#10312yes—
75C22×C101C2×C22⋊C411yescharacteristic
76C4×C101—21no—
77C4×C101—21no—
78C4×C101—41no—
79C4×C101—41no—
80Dic101—21no—
81Dic101—41no—
82Dic101—41no—
83Dic101#10312yes—
84Dic101C2×SD1611yescharacteristic
85Dic101C2×Q1611yescharacteristic
86Dic101AGL(1,ℤ/8)11yescharacteristic
87Dic101#13711yescharacteristic
88C2×C101—22no—
89C2×C101#41311yescharacteristic
90C2×C101C2×#10311yescharacteristic
91C2×C101#41711yescharacteristic
92#1550—1011nomaximal, Sylow
93C101#155011yescharacteristic, complemented, Sylow
94#533—1011no—
95#423—1011no—
96C2×C4⋊C8—1011no—
97#333—1012no—
98#332—1012no—
99C2×M16—2021no—
100C22×C8—2021no—
101C4⋊Q8—1011no—
102C4⋊Q8—1011no—
103#125—2021no—
104C22⋊Q8—1011no—
105C22⋊Q8—2021no—
106C22⋊Q8#8793811yescharacteristic
107C4×Q8—1011no—
108C4×Q8—1011no—
109C4×Q8—2021no—
110#117—2021no—
111C2×C42—1011no—
112C4⋊C8—1012no—
113C4⋊C8—1012no—
114C4⋊C8—2021no—
115C4⋊C8—2021no—
116C2×Q8—1011no—
117C2×Q8—2021no—
118C2×Q8C2×#8793811yescharacteristic
119C22×C4—1011no—
120C22×C4—1011no—
121C22×C4C2×#8793811yescharacteristic
122M16—4042no—
123C2×C8—4042no—
124C2×C8—2022no—
125C2×C8—2022no—
126C4⋊C4—21no—
127C4⋊C4—1011no—
128C4⋊C4—2021no—
129C4⋊C4—2021no—
130C4⋊C4—2021no—
131C4⋊C4—2021no—
132C4⋊C4—2021no—
133C4⋊C4—2021no—
134C4⋊C4C2×#8793811yescharacteristic
135C22⋊C4—21no—
136C22⋊C4—2021no—
137C42—1011no—
138C42—1011no—
139C42—1011no—
140C42—1011no—
141C42—2021no—
142C42—2021no—
143C23C22⋊#8793811yescharacteristic
144Q8—41no—
145Q8—4041no—
146Q8—4041no—
147Q8—4041no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—41no—
151C2×C4—1012no—
152C2×C4—1012no—
153C2×C4—1011no—
154C2×C4—1011no—
155C2×C4—1011no—
156C2×C4—1011no—
157C2×C4—2021no—
158C2×C4—2021no—
159C2×C4—2021no—
160C2×C4—2021no—
161C2×C4C22⋊#8793811yescharacteristic
162C2×C4C22×#8793811yescharacteristic
163C8—4042no—
164C8—4042no—
165C22—21no—
166C22—21no—
167C22#1569231812yes—
168C22C2×C22⋊#8793811yescharacteristic
169C4—21no—
170C4—21no—
171C4—41no—
172C4—41no—
173C4—1011no—
174C4—1012no—
175C4—1011no—
176C4—1011no—
177C4—1011no—
178C4—4041no—
179C4—4041no—
180C4—2021no—
181C2—22no—
182C2#2026616411yescharacteristic
183C2C2×#1569231811yescharacteristic
184C2#2026616811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#87938
commutatorC2×C4×C101C22×C4
FrattiniC2×C4C22×#87938
FittingC22⋊Q8×C101C4
socleC22×C101C2×C22⋊C4
prime radicalC23×C101C22⋊C4
cosocleC4×Dic101C23
hypercenterC22⋊Q8#87938
hypocenterC101#1550
LCSG ▷ C2×C4×C101 ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #20266037C2semidirect
4. #20266036C2semidirect
93. C101#1550semidirect

Maximal subgroups

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

subgroupindex
#202661802
C2×#156923222
#202660372
#202660362
#202657292
#1550101