Finite Group Databasebeta

← #27187424

Subgroups — #27187424

Order 12928.

250 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 52 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#20266164C212yesmaximal, complemented
2#20266088C212yesmaximal, complemented
3#20266085C212yesmaximal, complemented
4#20265725C211yesmaximal, characteristic
5C2×#13108083—22no—
6#15692316C2214yes—
7#15692315—22no—
8C2×#13108073C411yescharacteristic
9C2×#13108073C2211yescharacteristic
10#15692255C2211yescharacteristic
11#15692242C411yescharacteristic
12#15692242C2211yescharacteristic
13#15692226—22no—
14D4×Dic101—22no—
15C42×D101C411yescharacteristic
16#127×C101C411yescharacteristic
17#13108083—24no—
18#13108083—42no—
19C2×#11717581—42no—
20#13108073—41no—
21#13108073—41no—
22#13108073—41no—
23#13108073—41no—
24C2×Dic202C2×C411yescharacteristic
25C2×Dic202C2311yescharacteristic
26C2×C22⋊D101—21no—
27C2×C22⋊D101D412yes—
28C22×Dic101—21no—
29C22×Dic101D412yes—
30C2×C4×D101—21no—
31C2×C4×D101C2×C411yescharacteristic
32C4⋊Dic101—22no—
33C22⋊Dic101—22no—
34C22⋊Dic101—22no—
35C4×Dic101—21no—
36C4×Dic101C2×C411yescharacteristic
37C2×D4×C101—22no—
38C2×D4×C101C2×C411yescharacteristic
39C2×D4×C101C2×C411yescharacteristic
40C42×C101C2×C411yescharacteristic
41C23×C101—21no—
42C23×C101C22⋊C412yes—
43C22×D101C22⋊C411yescharacteristic
44D4×C101—41no—
45D4×C101—41no—
46D4×C101—44no—
47C2×C4×C101—21no—
48C2×C4×C101C22×C411yescharacteristic
49C22⋊D101—42no—
50C22⋊D101—42no—
51C2×Dic101—22no—
52C2×Dic101—22no—
53C2×Dic101—21no—
54C2×Dic101—21no—
55C2×Dic101—41no—
56C2×Dic101—41no—
57C2×Dic101C22⋊C411yescharacteristic
58C2×Dic101C2×D412yes—
59C4×D101—21no—
60C4×D101—21no—
61C4×D101—42no—
62Dic202—41no—
63Dic202—41no—
64#11717581—44no—
65C22×C101—22no—
66C22×C101—42no—
67C22×C101—42no—
68C22×C101—41no—
69C22×C101C2×C22⋊C411yescharacteristic
70C2×D101—21no—
71C2×D101—41no—
72C4×C101—22no—
73C4×C101—21no—
74Dic101—22no—
75Dic101—41no—
76Dic101—41no—
77Dic101#9911yescharacteristic
78Dic101#9911yescharacteristic
79C2×C101—21no—
80C2×C101—42no—
81C2×C101—81no—
82C2×C101C2×#9911yescharacteristic
83D101—41no—
84#2132—1011nomaximal, Sylow
85C101#213211yescharacteristic, complemented, Sylow
86#532—1011no—
87#413—1012no—
88#356—1012no—
89#355—1012no—
90C2×#41—1011no—
91C2×#41—1011no—
92C2×M16—2022no—
93C4⋊Q8—1011no—
94#127#8793811yescharacteristic
95#124—1011no—
96#124—1011no—
97#121—2022no—
98C4×D4—2022no—
99C2×C42—1011no—
100#101—1014no—
101#100—2022no—
102#41—4041no—
103#41—4041no—
104#41—4041no—
105#41—4041no—
106C2×Q8—1011no—
107C2×Q8—1011no—
108C2×D4—22no—
109C2×D4—1012no—
110C2×D4—2021no—
111C2×D4C2×#8793811yescharacteristic
112C2×D4C2×#8793811yescharacteristic
113C22×C4—1012no—
114C22×C4—1011no—
115C22×C4—2021no—
116C22×C4—2021no—
117M16—4042no—
118M16—2024no—
119C2×C8—4042no—
120C4⋊C4—2022no—
121C22⋊C4—2022no—
122C22⋊C4—2022no—
123C42—1011no—
124C42—2021no—
125C42C2×#8793811yescharacteristic
126C23—21no—
127C23—1011no—
128C23C22⋊#8793812yes—
129Q8—4041no—
130Q8—4041no—
131D4—41no—
132D4—41no—
133D4—44no—
134D4—4042no—
135D4—4042no—
136C2×C4—21no—
137C2×C4—1011no—
138C2×C4—1012no—
139C2×C4—4042no—
140C2×C4—4041no—
141C2×C4—4041no—
142C2×C4—2021no—
143C2×C4—2021no—
144C2×C4—2022no—
145C2×C4—2022no—
146C2×C4—2021no—
147C2×C4—2021no—
148C2×C4C22×#8793811yescharacteristic
149C8—4044no—
150C22—22no—
151C22—42no—
152C22—42no—
153C22—41no—
154C22—4041no—
155C22—2021no—
156C22C2×C22⋊#8793811yescharacteristic
157C4—22no—
158C4—21no—
159C4—1011no—
160C4—1011no—
161C4—4041no—
162C4—4041no—
163C4—2022no—
164C2—21no—
165C2—42no—
166C2—81no—
167C2—4041no—
168C2D101⋊#9911yescharacteristic
subgroupG/H
centerC2D101⋊#99
commutatorC2×C4×C101C22×C4
FrattiniC2×C4C22×#87938
Fitting#127×C101C4
socleC2×C101C2×#99
prime radical#20265725C2
cosocleC2×Dic202C23
hypercenter#127#87938
hypocenterC101#2132
LCSG ▷ C2×C4×C101 ▷ C22×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #20266164C2semidirect
2. #20266088C2semidirect
3. #20266085C2semidirect
85. C101#2132semidirect

Maximal subgroups

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

subgroupindex
#202661642
#202660882
#202660852
#202657252
#2132101