Finite Group Databasebeta

← #27187423

Subgroups — #27187423

Order 12928.

250 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 54 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#20266163C212yesmaximal, complemented
2#20266087C212yesmaximal, complemented
3#20266085C212yesmaximal, complemented
4#20265723C211yesmaximal, characteristic
5D101⋊M16—22no—
6#15692316C2214yes—
7#15692315—22no—
8C2×#13108074C2211yescharacteristic
9#15692253C2211yescharacteristic
10#15692251C411yescharacteristic
11#15692244C411yescharacteristic
12#15692242C2211yescharacteristic
13#15692227—22no—
14C4×C22⋊D101—22no—
15C2×C4×Dic101C411yescharacteristic
16C2×#41×C101C411yescharacteristic
17#13108084—42no—
18#13108083—24no—
19D101⋊C8—42no—
20#13108074—41no—
21#13108074—41no—
22C2×Dic202C2311yescharacteristic
23C2×D404C2×C411yescharacteristic
24C2×C22⋊D101—22no—
25C2×C22⋊D101D412yes—
26C22×Dic101—21no—
27C2×C4×D101D412yes—
28#13108053—22no—
29C22⋊Dic101—22no—
30#13108051—22no—
31C4×Dic101—21no—
32C4×Dic101C2×C411yescharacteristic
33C4×Dic101C2×C411yescharacteristic
34#41×C101—41no—
35#41×C101—41no—
36C2×Q8×C101C2×C411yescharacteristic
37C2×D4×C101—21no—
38C2×D4×C101C2×C411yescharacteristic
39C22×C4×C101—21no—
40C22×C4×C101C2×C411yescharacteristic
41C23×C101—21no—
42C23×C101C22⋊C411yescharacteristic
43C22×D101C22⋊C412yes—
44Q8×C101—41no—
45D4×C101—41no—
46D4×C101—42no—
47C2×C4×C101—21no—
48C2×C4×C101—21no—
49C2×C4×C101—21no—
50C2×C4×C101—41no—
51C2×C4×C101—41no—
52C2×C4×C101C22⋊C411yescharacteristic
53C2×C4×C101C22×C411yescharacteristic
54C22⋊D101—42no—
55C22⋊D101—44no—
56C2×Dic101—21no—
57C2×Dic101—21no—
58C2×Dic101—42no—
59C2×Dic101C2×D412yes—
60D404—41no—
61C4×D101—22no—
62C4×D101—22no—
63Dic202—41no—
64#11717581—44no—
65C22×C101—21no—
66C22×C101—41no—
67C22×C101—42no—
68C22×C101—41no—
69C22×C101C2×C22⋊C411yescharacteristic
70C2×D101—22no—
71C2×D101—42no—
72C4×C101—21no—
73C4×C101—41no—
74C4×C101#9911yescharacteristic
75C4×C101#9911yescharacteristic
76Dic101—22no—
77Dic101—22no—
78Dic101—41no—
79C2×C101—21no—
80C2×C101—41no—
81C2×C101—81no—
82C2×C101C2×#9911yescharacteristic
83D101—42no—
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#8793811yescharacteristic
92C2×M16—2022no—
93C4⋊Q8—1011no—
94#127—1011no—
95#124—1011no—
96#124—1011no—
97#121—2022no—
98C4×D4—2022no—
99C2×C42—1011no—
100#101—1014no—
101#100—2022no—
102#41—41no—
103#41—41no—
104#41—4041no—
105#41—4041no—
106C2×Q8—1011no—
107C2×Q8C2×#8793811yescharacteristic
108C2×D4—21no—
109C2×D4—1012no—
110C2×D4—1011no—
111C2×D4—2022no—
112C2×D4C2×#8793811yescharacteristic
113C22×C4—21no—
114C22×C4—1012no—
115C22×C4—2021no—
116C22×C4C2×#8793811yescharacteristic
117M16—4042no—
118M16—2024no—
119C2×C8—4042no—
120C4⋊C4—2022no—
121C22⋊C4—2022no—
122C22⋊C4—2022no—
123C42—1011no—
124C42—1011no—
125C42—2021no—
126C23—21no—
127C23—1012no—
128C23C22⋊#8793811yescharacteristic
129Q8—41no—
130Q8—4041no—
131D4—41no—
132D4—42no—
133D4—4041no—
134D4—4042no—
135D4—4044no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—21no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—1012no—
142C2×C4—4042no—
143C2×C4—2021no—
144C2×C4—2021no—
145C2×C4—2022no—
146C2×C4—2022no—
147C2×C4C22⋊#8793811yescharacteristic
148C2×C4C22×#8793811yescharacteristic
149C8—4044no—
150C22—21no—
151C22—41no—
152C22—42no—
153C22—41no—
154C22—4042no—
155C22—2022no—
156C22C2×C22⋊#8793811yescharacteristic
157C4—21no—
158C4—41no—
159C4—4041no—
160C4—2022no—
161C4—2022no—
162C4#1569231311yescharacteristic
163C4#1569231311yescharacteristic
164C2—21no—
165C2—41no—
166C2—81no—
167C2—4042no—
168C2C2×#1569231311yescharacteristic
subgroupG/H
centerC4#15692313
commutatorC2×C4×C101C22×C4
FrattiniC2×C4C22×#87938
FittingC2×#41×C101C4
socleC2×C101C2×#99
prime radical#20265723C2
cosocleC2×Dic202C23
hypercenterC2×#41#87938
hypocenterC101#2132
LCSG ▷ C2×C4×C101 ▷ C22×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #20266163C2semidirect
2. #20266087C2semidirect
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
#202661632
#202660872
#202660852
#202657232
#2132101