Finite Group Databasebeta

← #27186462

Subgroups — #27186462

Order 12928.

248 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 74 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#20266027C214yesmaximal, complemented
4C2×#15692220C211yesmaximal, characteristic
5C2×#13108083—21no—
6#15692322—21no—
7#15692322—21no—
8C4⋊#11717581C2212yes—
9C22⋊#11717581—21no—
10C4×#11717581C2212yes—
11C22×Dic202C411yescharacteristic
12#15692220—21no—
13#15692220—21no—
14#15692220C412yes—
15#15692220C2212yes—
16C2×#13108053—21no—
17C2×C4×Dic101—21no—
18C2×C4×Dic101C2211yescharacteristic
19C2×C4⋊C4×C101C411yescharacteristic
20#13108083—42no—
21C2×#11717581—22no—
22C2×#11717581—22no—
23C2×Dic202—21no—
24C2×Dic202—24no—
25C2×Dic202C2×C412yes—
26C22×Dic101—21no—
27C22×Dic101D411yescharacteristic
28C22×Dic101D411yescharacteristic
29#13108053—22no—
30#13108053—22no—
31C4×Dic101—22no—
32C4×Dic101—22no—
33C4×Dic101C2×C411yescharacteristic
34C4×Dic101D411yescharacteristic
35C4×Dic101D411yescharacteristic
36C4×Dic101C2311yescharacteristic
37C22×C4×C101—21no—
38C22×C4×C101C2×C411yescharacteristic
39C4⋊C4×C101—21no—
40C4⋊C4×C101C2×C412yes—
41C23×C101C22⋊C411yescharacteristic
42C2×C4×C101—22no—
43C2×C4×C101—22no—
44C2×C4×C101—42no—
45C2×C4×C101C22⋊C411yescharacteristic
46C2×C4×C101C22×C411yescharacteristic
47C2×Dic101—24no—
48C2×Dic101—22no—
49C2×Dic101—41no—
50C2×Dic101C22⋊C411yescharacteristic
51C2×Dic101C22⋊C411yescharacteristic
52C2×Dic101SD1612yes—
53C2×Dic101Q1612yes—
54C2×Dic101C2×D411yescharacteristic
55C2×Dic101C2×D411yescharacteristic
56Dic202—24no—
57Dic202—22no—
58Dic202M1614yescomplemented
59#11717581—42no—
60#11717581—42no—
61C22×C101—21no—
62C22×C101—21no—
63C22×C101#10312yes—
64C22×C101C2×C22⋊C411yescharacteristic
65C4×C101—21no—
66C4×C101—42no—
67C4×C101C2×M1612yes—
68Dic101—24no—
69Dic101—21no—
70Dic101—21no—
71Dic101#10312yes—
72Dic101C2×SD1611yescharacteristic
73Dic101C2×Q1611yescharacteristic
74C2×C101—22no—
75C2×C101#40711yescharacteristic
76C2×C101C2×#10311yescharacteristic
77C2×C101#42111yescharacteristic
78#1487—1011nomaximal, Sylow
79C101#148711yescharacteristic, complemented, Sylow
80C2×C4×Q8—1011no—
81#431—1011no—
82#423—1011no—
83Q8⋊C8—1014no—
84C22×Q8—1011no—
85C2×M16—2021no—
86C4×Q8—1012no—
87C4×Q8—1012no—
88C4×Q8—2021no—
89C4×Q8—2021no—
90C2×C4⋊C4—2021no—
91C2×C4⋊C4#8793811yescharacteristic
92C2×C42—1011no—
93C2×C42—2021no—
94C4⋊C8—1012no—
95C4⋊C8—2021no—
96C4⋊C8—2021no—
97C22⋊C8—2021no—
98C4×C8—1012no—
99C2×Q8—1012no—
100C2×Q8—2024no—
101C2×Q8—2021no—
102C22×C4—21no—
103C22×C4—1011no—
104C22×C4—1011no—
105C22×C4—2021no—
106C22×C4C2×#8793811yescharacteristic
107M16—4042no—
108C2×C8—2022no—
109C2×C8—2022no—
110C4⋊C4—21no—
111C4⋊C4—2022no—
112C4⋊C4—2022no—
113C4⋊C4C2×#8793812yes—
114C42—1011no—
115C42—1011no—
116C42—1011no—
117C42—1011no—
118C42—2022no—
119C42—2022no—
120C23C22⋊#8793811yescharacteristic
121Q8—1014no—
122Q8—2024no—
123Q8—2022no—
124C2×C4—22no—
125C2×C4—22no—
126C2×C4—42no—
127C2×C4—1012no—
128C2×C4—1012no—
129C2×C4—1011no—
130C2×C4—1011no—
131C2×C4—1011no—
132C2×C4—1011no—
133C2×C4—4041no—
134C2×C4—2024no—
135C2×C4—2022no—
136C2×C4C22⋊#8793811yescharacteristic
137C2×C4C22×#8793811yescharacteristic
138C8—4042no—
139C8—4042no—
140C22—21no—
141C22—21no—
142C22#1569231812yes—
143C22C2×C22⋊#8793811yescharacteristic
144C4—21no—
145C4—42no—
146C4—1011no—
147C4—1012no—
148C4—1011no—
149C4—2024no—
150C4—2021no—
151C4—2021no—
152C4D101⋊M1612yes—
153C2—22no—
154C2#2026614911yescharacteristic
155C2C2×#1569231811yescharacteristic
156C2#2026617511yescharacteristic
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#1487
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #20266027C2semidirect
58. Dic202M16semidirect
79. C101#1487semidirect

Maximal subgroups

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

subgroupindex
#202661942
#202661802
#202660272
C2×#156922202
#1487101