Finite Group Databasebeta

← #26527

Subgroups — #26527

Order 256.

341 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 341 conjugacy classes of subgroups — too many to draw. Only its 131 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#2571C211yesmaximal, characteristic
2#2365C211yesmaximal, characteristic
3#2097C212yesmaximal
4#2066C212yesmaximal
5#1981C211yesmaximal, characteristic
6#1956C211yesmaximal, characteristic
7#1948C211yesmaximal, characteristic
8#1939C211yesmaximal, characteristic
9#1863C212yesmaximal
10#1805C212yesmaximal
11C4×#107C211yesmaximal, characteristic
12C2×C4⋊Q8C2211yescharacteristic
13C2×C4×Q8C2212yes—
14C2×#107C2211yescharacteristic
15C2×#107C2211yescharacteristic
16C2×#106C2212yes—
17C2×C4⋊C8C2211yescharacteristic
18C2×C4⋊C8C2212yes—
19C2×#103C2212yes—
20C2×#103C2212yes—
21C2×#103C2212yes—
22C2×#103C2212yes—
23C2×C4×C8C2211yescharacteristic
24#400—22no—
25#391C2212yes—
26#389—21no—
27#389—21no—
28#389C2212yes—
29#387—22no—
30#384C2211yescharacteristic
31#382—21no—
32#382C2212yes—
33C4×C4⋊C4—21no—
34C4×C4⋊C4C2211yescharacteristic
35C4×C4⋊C4C2211yescharacteristic
36C4×C4⋊C4C2211yescharacteristic
37#340C2211yescharacteristic
38#340C2212yes—
39#340C2211yescharacteristic
40#336C2212yes—
41C22×Q8C2312yes—
42C22×C8C2312yes—
43C22×C8C2311yescharacteristic
44C22×C8C2311yescharacteristic
45C4⋊Q8—22no—
46C4⋊Q8Q814yes—
47C4×Q8—24no—
48C4×Q8—42no—
49C2×C4⋊C4—21no—
50C2×C4⋊C4—21no—
51C2×C4⋊C4—22no—
52C2×C4⋊C4—21no—
53C2×C4⋊C4—21no—
54C2×C4⋊C4—22no—
55C2×C4⋊C4D411yescharacteristic
56C2×C4⋊C4D411yescharacteristic
57C2×C4⋊C4C2311yescharacteristic
58C2×C4⋊C4C2311yescharacteristic
59C2×C4⋊C4C2311yescharacteristic
60C2×C4⋊C4C2312yes—
61C2×C4⋊C4C2311yescharacteristic
62C2×C42—22no—
63C2×C42—21no—
64C2×C42—21no—
65C2×C42C2312yes—
66C2×C42C2311yescharacteristic
67#107—22no—
68#107—22no—
69#106—42no—
70C4⋊C8—22no—
71C4⋊C8—42no—
72#103—24no—
73#103—42no—
74#103—42no—
75#103—42no—
76C4×C8—22no—
77#95—22no—
78#95—21no—
79#95—21no—
80#95—22no—
81#95—22no—
82#95—22no—
83#95—22no—
84#95D412yes—
85C2×Q8—22no—
86C2×Q8—22no—
87C2×Q8—22no—
88C2×Q8—22no—
89C2×Q8—22no—
90C2×Q8C2×Q814yes—
91C22×C4—22no—
92C22×C4—21no—
93C22×C4—21no—
94C22×C4—21no—
95C22×C4—21no—
96C22×C4—22no—
97C22×C4C2×D412yes—
98C22×C4C2×D412yes—
99C22×C4C2×D411yescharacteristic
100C22×C4C2×D411yescharacteristic
101C22×C4C2411yescharacteristic
102C2×C8—21no—
103C2×C8—21no—
104C2×C8—21no—
105C2×C8—22no—
106C2×C8—21no—
107C2×C8—22no—
108C2×C8—22no—
109C2×C8—21no—
110C2×C8#4112yes—
111C4⋊C4—24no—
112C4⋊C4—24no—
113C4⋊C4—22no—
114C4⋊C4—22no—
115C4⋊C4—21no—
116C4⋊C4—22no—
117C4⋊C4—21no—
118C4⋊C4—21no—
119C4⋊C4—21no—
120C4⋊C4—21no—
121C4⋊C4—21no—
122C4⋊C4—22no—
123C4⋊C4—21no—
124C4⋊C4—44no—
125C4⋊C4—42no—
126C4⋊C4—81no—
127C4⋊C4—82no—
128C4⋊C4#4112yes—
129C42—22no—
130C42—22no—
131C42—44no—
132C42—42no—
133C42—42no—
134C42C2×Q812yes—
135C42#4112yes—
136C23C22×D411yescharacteristic
137Q8—24no—
138Q8—24no—
139Q8—42no—
140Q8—42no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—24no—
144C2×C4—22no—
145C2×C4—22no—
146C2×C4—22no—
147C2×C4—22no—
148C2×C4—22no—
149C2×C4—22no—
150C2×C4—22no—
151C2×C4—42no—
152C2×C4—42no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—42no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4C22⋊Q812yes—
168C2×C4C22⋊Q812yes—
169C2×C4#13512yes—
170C2×C4#13712yes—
171C2×C4C22×Q811yescharacteristic
172C2×C4C2×#4111yescharacteristic
173C2×C4C2×#4111yescharacteristic
174C2×C4C2×#4111yescharacteristic
175C2×C4H(5,𝔽2)11yescharacteristic
176C2×C4H(5,𝔽2)11yescharacteristic
177C8—22no—
178C8—41no—
179C8—42no—
180C22C2×C22⋊Q811yescharacteristic
181C22#54611yescharacteristic
182C22#55011yescharacteristic
183C22C2×#13511yescharacteristic
184C22C2×#13711yescharacteristic
185C22#57711yescharacteristic
186C22#57811yescharacteristic
187C4—22no—
188C4—42no—
189C4—44no—
190C4—42no—
191C4—42no—
192C4—81no—
193C4—81no—
194C4—82no—
195C4—81no—
196C4#47914yes—
197C4#52911yescharacteristic
198C4#54011yescharacteristic
199C4#55411yescharacteristic
200C4#55411yescharacteristic
201C2#245411yescharacteristic
202C2C2×#47911yescharacteristic
203C2#308211yescharacteristic
204C2#330311yescharacteristic
205C2#332811yescharacteristic
206C2#339311yescharacteristic
207C2#340011yescharacteristic
subgroupG/H
center, socle, prime radicalC23C22×D4
commutator, Frattini, cosocleC22×C4C24
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
#25712
#23652
#20972
#20662
#19812
#19562
#19482
#19392
#18632
#18052
C4×#1072