Finite Group Databasebeta

← #27172296

Subgroups — #27172296

Order 12928.

466 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 69 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#20265803C211yesmaximal, characteristic, complemented
2#20265033C212yesmaximal
3#20264944C211yesmaximal, characteristic, complemented
4#20264943C212yesmaximal, complemented
5#379×C101C211yesmaximal, characteristic
6#15692234—22no—
7#15692232—24no—
8C2×C22⋊Dic101—24no—
9C2×C22⋊Dic101C2212yes—
10C2×C22⋊Dic101C2212yes—
11C25×C101C2211yescharacteristic
12C2×C22⋊C4×C101—22no—
13C2×C22⋊C4×C101C2211yescharacteristic
14C2×C22⋊C4×C101C2211yescharacteristic
15C2×Dic202—22no—
16C22×Dic101—22no—
17C22×Dic101D414yes—
18C4⋊Dic101—22no—
19#13108053—24no—
20C22⋊Dic101—22no—
21C22⋊Dic101—22no—
22C22⋊Dic101—22no—
23C22⋊Dic101—22no—
24C22⋊Dic101—48no—
25C24×C101—21no—
26C24×C101—22no—
27C24×C101—22no—
28C24×C101—21no—
29C24×C101—44no—
30C24×C101Q812yescomplemented
31C24×C101C2311yescharacteristic
32C22×C4×C101—21no—
33C22×C4×C101D412yes—
34C22⋊C4×C101—22no—
35C22⋊C4×C101—22no—
36C22⋊C4×C101—44no—
37C23×C101—24no—
38C23×C101—28no—
39C23×C101—24no—
40C23×C101—22no—
41C23×C101—44no—
42C23×C101—42no—
43C23×C101—44no—
44C23×C101—42no—
45C23×C101—48no—
46C23×C101—44no—
47C23×C101—41no—
48C23×C101—42no—
49C23×C101—41no—
50C23×C101C2×D412yes—
51C23×C101C2×D411yescharacteristic
52C23×C101C2×Q811yescharacteristic
53C23×C101#4112yes—
54C23×C101#4111yescharacteristic
55C2×C4×C101—22no—
56C2×C4×C101—42no—
57C2×C4×C101—42no—
58C2×C4×C101—41no—
59C2×Dic101—24no—
60C2×Dic101—44no—
61C2×Dic101—44no—
62C2×Dic101—42no—
63Dic202—82no—
64C22×C101—24no—
65C22×C101—22no—
66C22×C101—24no—
67C22×C101—28no—
68C22×C101—41no—
69C22×C101—42no—
70C22×C101—41no—
71C22×C101—48no—
72C22×C101—44no—
73C22×C101—44no—
74C22×C101—42no—
75C22×C101—42no—
76C22×C101—44no—
77C22×C101#12011yescharacteristic
78C22×C101C22⋊Q812yes—
79C22×C101C22⋊Q811yescharacteristic
80C22×C101#12412yes—
81C22×C101#12411yescharacteristic
82C4×C101—42no—
83C4×C101—81no—
84Dic101—44no—
85Dic101—82no—
86C2×C101—22no—
87C2×C101—21no—
88C2×C101—22no—
89C2×C101—21no—
90C2×C101—44no—
91C2×C101#39311yescharacteristic
92C2×C101B(4,𝔽2)12yes—
93#2029—1011nomaximal, Sylow
94C101#202911yescharacteristic, complemented, Sylow
95#543—1011no—
96#379—1012no—
97#379D10111yescharacteristic
98#342—1012no—
99#342—1011no—
100C25C2×D10111yescharacteristic
101C22⋊Q8—2024no—
102C22⋊Q8—2022no—
103C2×C22⋊C4—22no—
104C2×C22⋊C4—1012no—
105C2×C22⋊C4—1012no—
106C2×C22⋊C4—2024no—
107C2×C22⋊C4C2×D10111yescharacteristic
108C2×C22⋊C4C2×D10111yescharacteristic
109C24—22no—
110C24—21no—
111C24—22no—
112C24—21no—
113C24—44no—
114C24Dic20212yescomplemented
115C24C22×D10111yescharacteristic
116C2×Q8—2022no—
117C22×C4—21no—
118C22×C4—1014no—
119C22×C4—2022no—
120C22×C4C22⋊D10112yes—
121C4⋊C4—2024no—
122C4⋊C4—2022no—
123C22⋊C4—22no—
124C22⋊C4—22no—
125C22⋊C4—44no—
126C22⋊C4—4048no—
127C22⋊C4—2022no—
128C22⋊C4—2022no—
129C22⋊C4—2022no—
130C22⋊C4—2022no—
131C23—24no—
132C23—28no—
133C23—24no—
134C23—22no—
135C23—44no—
136C23—42no—
137C23—42no—
138C23—44no—
139C23—48no—
140C23—44no—
141C23—41no—
142C23—42no—
143C23—41no—
144C23D4×D10112yes—
145C23C2×C22⋊D10111yescharacteristic
146C23C2×Dic20211yescharacteristic
147C23#1310807312yes—
148C23#1310807411yescharacteristic
149Q8—8082no—
150C2×C4—22no—
151C2×C4—42no—
152C2×C4—42no—
153C2×C4—41no—
154C2×C4—4044no—
155C2×C4—4042no—
156C2×C4—4044no—
157C2×C4—2024no—
158C22—22no—
159C22—24no—
160C22—28no—
161C22—24no—
162C22—41no—
163C22—42no—
164C22—41no—
165C22—44no—
166C22—48no—
167C22—44no—
168C22—42no—
169C22—42no—
170C22—44no—
171C22#1569222311yescharacteristic
172C22#1569223212yes—
173C22#1569223411yescharacteristic
174C22#1569224112yes—
175C22#1569224211yescharacteristic
176C4—42no—
177C4—81no—
178C4—8082no—
179C4—4044no—
180C2—21no—
181C2—22no—
182C2—22no—
183C2—21no—
184C2—44no—
185C2#2026508911yescharacteristic
186C2#2026536312yes—
subgroupG/H
centerC22#15692223
commutator, cosocleC24×C101C23
FrattiniC24C22×D101
Fitting#379×C101C2
socleC22×C101#120
prime radicalC25×C101C22
hypercenter#379D101
hypocenterC101#2029
LCSG ▷ C24×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C24 ◁ #379

Complements

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

NH ≅ G/Ntype
1. #20265803C2semidirect
3. #20264944C2semidirect
4. #20264943C2semidirect
30. C24×C101Q8semidirect
94. C101#2029semidirect
114. C24Dic202semidirect

Maximal subgroups

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

subgroupindex
#202658032
#202650332
#202649442
#202649432
#379×C1012
#2029101