Finite Group Databasebeta

← #27172273

Subgroups — #27172273

Order 12928.

290 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 93 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
1C2×#15692255C211yesmaximal, characteristic
2C2×#15692179C212yesmaximal
3#20264939C212yesmaximal
4#20264932C211yesmaximal, characteristic
5#391×C101C211yesmaximal, characteristic
6C22×Dic202—21no—
7C22×#11717579C2212yes—
8#15692255—24no—
9C2×C4⋊Dic101—21no—
10C2×C4⋊Dic101C2212yes—
11#15692179—24no—
12C22×Q8×C101C2211yescharacteristic
13C2×C4⋊C4×C101C2211yescharacteristic
14C2×C42×C101C2211yescharacteristic
15#95×C101—21no—
16#95×C101—21no—
17C2×Dic202—24no—
18C2×Dic202—42no—
19C2×Dic202—42no—
20C22×Dic101—22no—
21C2×#11717579—22no—
22C2×#11717579—22no—
23C2×#11717579—22no—
24C4⋊Dic101—24no—
25C4⋊Dic101—22no—
26C4⋊Dic101D414yes—
27C2×Q8×C101—21no—
28C2×Q8×C101—22no—
29C2×Q8×C101—22no—
30C2×Q8×C101Q812yescomplemented
31C22×C4×C101—21no—
32C22×C4×C101—21no—
33C22×C4×C101D411yescharacteristic
34C22×C4×C101D411yescharacteristic
35C22×C4×C101C2311yescharacteristic
36C4⋊C4×C101—22no—
37C42×C101—22no—
38C23×C101C2×D411yescharacteristic
39Q8×C101—24no—
40Q8×C101—42no—
41C2×C4×C101—21no—
42C2×C4×C101—21no—
43C2×C4×C101—21no—
44C2×C4×C101—21no—
45C2×C4×C101—22no—
46C2×C4×C101—41no—
47C2×C4×C101—41no—
48C2×C4×C101—41no—
49C2×C4×C101—41no—
50C2×C4×C101—41no—
51C2×C4×C101SD1612yes—
52C2×C4×C101Q1612yes—
53C2×C4×C101C2×D412yes—
54C2×C4×C101C2×Q811yescharacteristic
55C2×C4×C101#4112yes—
56C2×C4×C101#4111yescharacteristic
57C2×Dic101—24no—
58C2×Dic101—42no—
59C2×Dic101—42no—
60Dic202—48no—
61#11717579—42no—
62C22×C101#12011yescharacteristic
63C22×C101C22⋊Q811yescharacteristic
64C22×C101#12411yescharacteristic
65C22×C101C2×SD1611yescharacteristic
66C22×C101C2×Q1611yescharacteristic
67C22×C101AGL(1,ℤ/8)11yescharacteristic
68C22×C101#13711yescharacteristic
69C4×C101—22no—
70C4×C101—22no—
71C4×C101—42no—
72C4×C101—81no—
73C4×C101C22⋊Q812yes—
74C4×C101#12412yes—
75Dic101—44no—
76C2×C101#39311yescharacteristic
77C2×C101#45011yescharacteristic
78C2×C101#45111yescharacteristic
79C2×C101#47511yescharacteristic
80C2×C101#47711yescharacteristic
81C2×C101#48711yescharacteristic
82C2×C101#48911yescharacteristic
83#2024—1011nomaximal, Sylow
84C101#202411yescharacteristic, complemented, Sylow
85C2×C4⋊Q8—1011no—
86C2×#103—1012no—
87#391D10111yescharacteristic
88#340—1012no—
89#336—1011no—
90C22×Q8—2021no—
91C22×Q8C2×D10111yescharacteristic
92C22×C8—1012no—
93C4⋊Q8—2024no—
94C2×C4⋊C4—1012no—
95C2×C4⋊C4—2021no—
96C2×C4⋊C4C2×D10111yescharacteristic
97C2×C42C2×D10111yescharacteristic
98#103—2024no—
99#95—21no—
100#95—21no—
101C2×Q8—21no—
102C2×Q8—22no—
103C2×Q8—22no—
104C2×Q8—4042no—
105C2×Q8—4042no—
106C2×Q8—2024no—
107C2×Q8Dic20212yescomplemented
108C22×C4—21no—
109C22×C4—21no—
110C22×C4—2022no—
111C22×C4C22⋊D10111yescharacteristic
112C22×C4C22⋊D10111yescharacteristic
113C22×C4C22×D10111yescharacteristic
114C2×C8—2022no—
115C2×C8—2022no—
116C2×C8—2022no—
117C4⋊C4—22no—
118C4⋊C4—1014no—
119C4⋊C4—2024no—
120C4⋊C4—2022no—
121C42—22no—
122C23C2×C22⋊D10111yescharacteristic
123Q8—24no—
124Q8—42no—
125Q8—4048no—
126C2×C4—21no—
127C2×C4—21no—
128C2×C4—21no—
129C2×C4—21no—
130C2×C4—22no—
131C2×C4—41no—
132C2×C4—41no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—41no—
136C2×C4—4042no—
137C2×C4—4042no—
138C2×C4—2024no—
139C2×C4#1310806112yes—
140C2×C4#1310806412yes—
141C2×C4D4×D10112yes—
142C2×C4C2×Dic20211yescharacteristic
143C2×C4#1310807312yes—
144C2×C4#1310807411yescharacteristic
145C8—4042no—
146C22#1569222311yescharacteristic
147C22#1569223411yescharacteristic
148C22#1569224211yescharacteristic
149C22C2×#1310806111yescharacteristic
150C22C2×#1310806411yescharacteristic
151C22#1569228011yescharacteristic
152C22#1569228511yescharacteristic
153C4—22no—
154C4—22no—
155C4—42no—
156C4—81no—
157C4—4044no—
158C4#1569223212yes—
159C4#1569224112yes—
160C2#2026508911yescharacteristic
161C2#2026532711yescharacteristic
162C2#2026533211yescharacteristic
163C2#2026546211yescharacteristic
164C2#2026547211yescharacteristic
165C2#2026552711yescharacteristic
166C2#2026553611yescharacteristic
subgroupG/H
centerC23C2×C22⋊D101
commutator, cosocleC22×C4×C101C23
FrattiniC22×C4C22×D101
Fitting#391×C101C2
socle, prime radicalC23×C101C2×D4
hypercenter#391D101
hypocenterC101#2024
LCSG ▷ C22×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
30. C2×Q8×C101Q8semidirect
84. C101#2024semidirect
107. C2×Q8Dic202semidirect

Maximal subgroups

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

subgroupindex
C2×#156922552
C2×#156921792
#202649392
#202649322
#391×C1012
#2024101