Finite Group Databasebeta

← #27181262

Subgroups — #27181262

Order 12928.

380 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 133 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#20265734C211yesmaximal, characteristic
2#20265507C212yesmaximal
3#20265462C212yesmaximal, complemented
4#20265387C212yesmaximal, complemented
5#20265333C212yesmaximal
6#20265282C214yesmaximal, complemented
7#20265234C211yesmaximal, characteristic
8C2×C4×Q8×C101C211yesmaximal, characteristic
9C2×#13108064C2214yes—
10#15692255C2211yescharacteristic
11#15692255C2211yescharacteristic
12#15692247—21no—
13#15692234—21no—
14#15692234C2212yes—
15C4×Dic202—21no—
16C4×Dic202C2212yes—
17#15692214—21no—
18#15692186C2214yes—
19C4⋊#11717579C2212yes—
20#15692179C2214yes—
21#15692178C2214yes—
22C22⋊#11717579C2212yes—
23#15692166C2212yes—
24C22×Q8×C101C2211yescharacteristic
25C4×Q8×C101—21no—
26C4×Q8×C101—21no—
27C4×Q8×C101C2212yes—
28C4×Q8×C101C2212yes—
29C2×C4⋊C4×C101—21no—
30C2×C4⋊C4×C101C2211yescharacteristic
31C2×C42×C101—21no—
32C2×C42×C101C2211yescharacteristic
33C2×Dic202—21no—
34C2×Dic202C2312yes—
35#13108064—28no—
36C2×#11717579C2314yes—
37C4⋊Dic101—21no—
38C4⋊Dic101—21no—
39C4⋊Dic101—21no—
40C4⋊Dic101C2312yes—
41#13108053—22no—
42#13108053—22no—
43C22⋊Dic101—22no—
44C4×Dic101—22no—
45C2×Q8×C101—24no—
46C2×Q8×C101—21no—
47C2×Q8×C101C2312yes—
48C22×C4×C101—21no—
49C22×C4×C101—21no—
50C22×C4×C101D411yescharacteristic
51C22×C4×C101D411yescharacteristic
52C22×C4×C101C2311yescharacteristic
53C4⋊C4×C101—22no—
54C4⋊C4×C101—22no—
55C4⋊C4×C101—21no—
56C4⋊C4×C101C2312yes—
57C42×C101—22no—
58C42×C101—22no—
59C42×C101D411yescharacteristic
60C42×C101D411yescharacteristic
61C42×C101C2311yescharacteristic
62C42×C101C2311yescharacteristic
63C23×C101C2×D411yescharacteristic
64Q8×C101—24no—
65Q8×C101—22no—
66Q8×C101#4114yes—
67C2×C4×C101—24no—
68C2×C4×C101—22no—
69C2×C4×C101—22no—
70C2×C4×C101—22no—
71C2×C4×C101—22no—
72C2×C4×C101—22no—
73C2×C4×C101—42no—
74C2×C4×C101C2×D411yescharacteristic
75C2×C4×C101C2×D411yescharacteristic
76C2×C4×C101C2×D411yescharacteristic
77C2×C4×C101C2×D411yescharacteristic
78C2×C4×C101C2×D411yescharacteristic
79C2×C4×C101C2411yescharacteristic
80C2×Dic101—22no—
81C2×Dic101—22no—
82Dic202—24no—
83Dic202—42no—
84#11717579—24no—
85C22×C101—21no—
86C22×C101—21no—
87C22×C101#13712yes—
88C22×C101C22×D411yescharacteristic
89C4×C101—24no—
90C4×C101—21no—
91C4×C101—21no—
92C4×C101—21no—
93C4×C101—21no—
94C4×C101—42no—
95C4×C101#13712yes—
96C4×C101C2×#4112yes—
97Dic101—42no—
98Dic101—42no—
99C2×C101—22no—
100C2×C101#52511yescharacteristic
101C2×C101C2×#13711yescharacteristic
102C2×C101C2×#13711yescharacteristic
103#3113—1011nomaximal, Sylow
104C101#311311yescharacteristic, complemented, Sylow
105#533—1011no—
106C2×C4×Q8D10111yescharacteristic
107#483—1012no—
108#475—1012no—
109#462—1012no—
110#451—1012no—
111#441—1014no—
112#432—1011no—
113C22×Q8C2×D10111yescharacteristic
114C2×Q16—1014no—
115C4⋊Q8—1011no—
116C4⋊Q8—1011no—
117#125—2021no—
118C22⋊Q8—1012no—
119C22⋊Q8—2021no—
120C4×Q8—21no—
121C4×Q8—21no—
122C4×Q8—1012no—
123C4×Q8—2021no—
124C4×Q8C2×D10112yes—
125C4×Q8C2×D10112yes—
126#117—2021no—
127C2×C4⋊C4—21no—
128C2×C4⋊C4C2×D10111yescharacteristic
129C2×C42—21no—
130C2×C42C2×D10111yescharacteristic
131#106—1014no—
132C4⋊C8—1012no—
133#103—1014no—
134#103—1014no—
135C22⋊C8—1012no—
136#97—1012no—
137C2×Q8—24no—
138C2×Q8—21no—
139C2×Q8—1012no—
140C2×Q8—2021no—
141C2×Q8C22×D10112yes—
142C22×C4—21no—
143C22×C4—21no—
144C22×C4C22⋊D10111yescharacteristic
145C22×C4C22⋊D10111yescharacteristic
146C22×C4C22×D10111yescharacteristic
147Q16—2028no—
148C2×C8—1014no—
149C4⋊C4—22no—
150C4⋊C4—22no—
151C4⋊C4—21no—
152C4⋊C4—1012no—
153C4⋊C4—2022no—
154C4⋊C4—2022no—
155C4⋊C4—2021no—
156C4⋊C4—2021no—
157C4⋊C4—2021no—
158C4⋊C4C22×D10112yes—
159C22⋊C4—2022no—
160C42—22no—
161C42—22no—
162C42—2022no—
163C42C22⋊D10111yescharacteristic
164C42C22⋊D10111yescharacteristic
165C42C22×D10111yescharacteristic
166C42C22×D10111yescharacteristic
167C23C2×C22⋊D10111yescharacteristic
168Q8—24no—
169Q8—22no—
170Q8—4042no—
171Q8—2024no—
172Q8#1310807414yes—
173C2×C4—24no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—42no—
180C2×C4—2022no—
181C2×C4—2022no—
182C2×C4C2×C22⋊D10111yescharacteristic
183C2×C4C2×C22⋊D10111yescharacteristic
184C2×C4C2×C22⋊D10111yescharacteristic
185C2×C4C2×C22⋊D10111yescharacteristic
186C2×C4C2×C22⋊D10111yescharacteristic
187C2×C4C23×D10111yescharacteristic
188C8—2024no—
189C22—21no—
190C22—21no—
191C22#1569228512yes—
192C22C22×C22⋊D10111yescharacteristic
193C4—24no—
194C4—21no—
195C4—21no—
196C4—21no—
197C4—21no—
198C4—42no—
199C4—4042no—
200C4—4042no—
201C4#1569228612yes—
202C4C2×#1310807412yes—
203C2—22no—
204C2#2026568811yescharacteristic
205C2C2×#1569228511yescharacteristic
206C2C2×#1569228611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
FittingC2×C4×Q8×C101C2
socleC22×C101C22×D4
prime radicalC23×C101C2×D4
hypercenterC2×C4×Q8D101
hypocenterC101#3113
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
3. #20265462C2semidirect
4. #20265387C2semidirect
6. #20265282C2semidirect
104. C101#3113semidirect

Maximal subgroups

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

subgroupindex
#202657342
#202655072
#202654622
#202653872
#202653332
#202652822
#202652342
C2×C4×Q8×C1012
#3113101