Finite Group Databasebeta

← #27186641

Subgroups — #27186641

Order 12928.

240 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 72 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#20266194C211yesmaximal, characteristic
2#20266180C211yesmaximal, characteristic
3#20266036C214yesmaximal, complemented
4C2×#15692254C211yesmaximal, characteristic
5C2×#13108083—21no—
6#15692322C2212yes—
7#15692322C2212yes—
8C4⋊#11717581—21no—
9C22⋊#11717581—21no—
10C4×#11717581—21no—
11C22×Dic202—21no—
12#15692254—21no—
13#15692254—21no—
14#15692254C412yes—
15#15692254C2212yes—
16C2×C4⋊Dic101C411yescharacteristic
17C2×#13108053—21no—
18C2×C4×Dic101C2211yescharacteristic
19C2×C4⋊C4×C101C411yescharacteristic
20#13108083—42no—
21C2×#11717581—22no—
22C2×#11717581—22no—
23C2×Dic202—22no—
24C2×Dic202—22no—
25C2×Dic202—42no—
26C2×Dic202—42no—
27C22×Dic101—21no—
28C22×Dic101D411yescharacteristic
29C22×Dic101D411yescharacteristic
30C4⋊Dic101—21no—
31C4⋊Dic101C2×C412yes—
32#13108053—22no—
33#13108053—22no—
34C4×Dic101C2×C411yescharacteristic
35C4×Dic101D411yescharacteristic
36C4×Dic101D411yescharacteristic
37C4×Dic101C2311yescharacteristic
38C22×C4×C101—21no—
39C22×C4×C101C2×C411yescharacteristic
40C4⋊C4×C101—21no—
41C4⋊C4×C101C2×C412yes—
42C23×C101C22⋊C411yescharacteristic
43C2×C4×C101—22no—
44C2×C4×C101—22no—
45C2×C4×C101—42no—
46C2×C4×C101C22⋊C411yescharacteristic
47C2×C4×C101C22×C411yescharacteristic
48C2×Dic101—22no—
49C2×Dic101—22no—
50C2×Dic101—42no—
51C2×Dic101C22⋊C411yescharacteristic
52C2×Dic101C22⋊C411yescharacteristic
53C2×Dic101D812yes—
54C2×Dic101SD1612yes—
55C2×Dic101C2×D411yescharacteristic
56C2×Dic101C2×D411yescharacteristic
57Dic202—44no—
58Dic202—42no—
59Dic202—42no—
60#11717581—42no—
61#11717581—42no—
62C22×C101—21no—
63C22×C101—21no—
64C22×C101#10212yes—
65C22×C101C2×C22⋊C411yescharacteristic
66C4×C101—21no—
67C4×C101—42no—
68C4×C101#10112yes—
69Dic101—21no—
70Dic101—42no—
71Dic101#10212yes—
72Dic101C2×D811yescharacteristic
73Dic101C2×SD1611yescharacteristic
74Dic101#13712yes—
75C2×C101—22no—
76C2×C101C2×#10111yescharacteristic
77C2×C101C2×#10211yescharacteristic
78C2×C101#41911yescharacteristic
79#1546—1011nomaximal, Sylow
80C101#154611yescharacteristic, complemented, Sylow
81C2×C4⋊Q8—1011no—
82#431—1011no—
83#423—1011no—
84#332—1014no—
85C22×Q8—2021no—
86C2×M16—2021no—
87C4⋊Q8—1012no—
88C4⋊Q8—1012no—
89C4⋊Q8—2021no—
90C4⋊Q8—2021no—
91C2×C4⋊C4—1011no—
92C2×C4⋊C4—2021no—
93C2×C4⋊C4#8793811yescharacteristic
94C2×C42—1011no—
95C4⋊C8—1012no—
96C4⋊C8—1012no—
97C4⋊C8—2021no—
98C22⋊C8—2021no—
99C4×C8—2021no—
100C2×Q8—4042no—
101C2×Q8—4042no—
102C2×Q8—2022no—
103C2×Q8—2022no—
104C22×C4—21no—
105C22×C4—1011no—
106C22×C4—1011no—
107C22×C4—2021no—
108C22×C4C2×#8793811yescharacteristic
109M16—4042no—
110C2×C8—2022no—
111C2×C8—2022no—
112C4⋊C4—21no—
113C4⋊C4—1012no—
114C4⋊C4—2022no—
115C4⋊C4—2022no—
116C4⋊C4—2021no—
117C4⋊C4C2×#8793812yes—
118C42—1011no—
119C42—1011no—
120C42—1011no—
121C42—1011no—
122C23C22⋊#8793811yescharacteristic
123Q8—4042no—
124Q8—4044no—
125Q8—4042no—
126C2×C4—22no—
127C2×C4—22no—
128C2×C4—42no—
129C2×C4—1012no—
130C2×C4—1012no—
131C2×C4—1011no—
132C2×C4—1011no—
133C2×C4—1011no—
134C2×C4—1011no—
135C2×C4—4042no—
136C2×C4—2022no—
137C2×C4—2022no—
138C2×C4C22⋊#8793811yescharacteristic
139C2×C4C22×#8793811yescharacteristic
140C8—4042no—
141C8—4042no—
142C22—21no—
143C22—21no—
144C22#1569231712yes—
145C22C2×C22⋊#8793811yescharacteristic
146C4—21no—
147C4—42no—
148C4—1011no—
149C4—1012no—
150C4—1011no—
151C4—1012no—
152C4—4042no—
153C4—2021no—
154C4#1569231612yes—
155C2—22no—
156C2C2×#1569231611yescharacteristic
157C2C2×#1569231711yescharacteristic
158C2#2026617011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#87938
commutatorC2×C4×C101C22×C4
FrattiniC2×C4C22×#87938
FittingC2×C4⋊C4×C101C4
socleC22×C101C2×C22⋊C4
prime radicalC23×C101C22⋊C4
cosocleC4×Dic101C23
hypercenterC2×C4⋊C4#87938
hypocenterC101#1546
LCSG ▷ C2×C4×C101 ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #20266036C2semidirect
80. C101#1546semidirect

Maximal subgroups

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

subgroupindex
#202661942
#202661802
#202660362
C2×#156922542
#1546101