Finite Group Databasebeta

← #29875

Subgroups — #29875

Order 256.

330 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 119 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×#479C211yesmaximal, characteristic
2C2×#477C211yesmaximal, characteristic
3#2660C211yesmaximal, characteristic
4#2320C211yesmaximal, characteristic
5#2085C212yesmaximal
6#2083C212yesmaximal
7#2074C212yesmaximal
8#2072C212yesmaximal
9#1989C211yesmaximal, characteristic
10#1988C211yesmaximal, characteristic
11#1832C211yesmaximal, characteristic
12C2×C4⋊Q8C2211yescharacteristic
13C2×#125C2211yescharacteristic
14C2×C4×Q8C2211yescharacteristic
15#479—24no—
16#477—24no—
17C2×#107C2212yes—
18C2×#107C2211yescharacteristic
19C2×#106C2211yescharacteristic
20C2×C4⋊C8C2211yescharacteristic
21C2×C4⋊C8C2211yescharacteristic
22C2×#103C2212yes—
23C2×#103C2211yescharacteristic
24C2×#103C2211yescharacteristic
25#398—21no—
26#398—21no—
27#395—22no—
28#391C2212yes—
29#389C2212yes—
30#387—22no—
31#384C2212yes—
32#383—21no—
33#382—21no—
34#382C2212yes—
35C4×C4⋊C4C2211yescharacteristic
36#376C2211yescharacteristic
37#340C2212yes—
38#340C2212yes—
39#340C2212yes—
40#340C2212yes—
41#336C2212yes—
42#336C2212yes—
43C22×Q8—21no—
44C22×Q8C2311yescharacteristic
45C22×C8C2311yescharacteristic
46C22×C8C2312yes—
47C22×C8C2311yescharacteristic
48C4⋊Q8—22no—
49C4⋊Q8—22no—
50#125—22no—
51#125—22no—
52C4×Q8—22no—
53C4×Q8D414yes—
54C2×C4⋊C4—21no—
55C2×C4⋊C4—21no—
56C2×C4⋊C4—21no—
57C2×C4⋊C4—21no—
58C2×C4⋊C4—22no—
59C2×C4⋊C4—22no—
60C2×C4⋊C4—22no—
61C2×C4⋊C4C2311yescharacteristic
62C2×C4⋊C4C2311yescharacteristic
63C2×C4⋊C4C2312yes—
64C2×C4⋊C4C2312yes—
65C2×C4⋊C4C2311yescharacteristic
66C2×C42—21no—
67C2×C42—21no—
68C2×C42C2312yes—
69C2×C42C2311yescharacteristic
70#107—24no—
71#107—22no—
72#106—22no—
73C4⋊C8—22no—
74C4⋊C8—22no—
75#103—24no—
76#103—22no—
77#103—22no—
78#95—21no—
79#95—22no—
80#95—22no—
81#95—22no—
82#95—22no—
83#95—22no—
84#95D411yescharacteristic
85#95D411yescharacteristic
86#95D412yes—
87C2×Q8—21no—
88C2×Q8—22no—
89C2×Q8—22no—
90C2×Q8—42no—
91C2×Q8—81no—
92C2×Q8—81no—
93C2×Q8C2×D412yes—
94C22×C4—21no—
95C22×C4—21no—
96C22×C4—22no—
97C22×C4—21no—
98C22×C4—22no—
99C22×C4—21no—
100C22×C4C2×D412yes—
101C22×C4C2×D412yes—
102C22×C4C2×D411yescharacteristic
103C22×C4C2×D411yescharacteristic
104C22×C4C2411yescharacteristic
105C2×C8—21no—
106C2×C8—22no—
107C2×C8—21no—
108C2×C8—22no—
109C2×C8—24no—
110C2×C8—22no—
111C4⋊C4—24no—
112C4⋊C4—21no—
113C4⋊C4—21no—
114C4⋊C4—21no—
115C4⋊C4—22no—
116C4⋊C4—21no—
117C4⋊C4—21no—
118C4⋊C4—22no—
119C4⋊C4—22no—
120C4⋊C4—22no—
121C4⋊C4—42no—
122C4⋊C4—42no—
123C4⋊C4—42no—
124C4⋊C4—82no—
125C4⋊C4—82no—
126C4⋊C4—82no—
127C4⋊C4C2×D412yes—
128C42—24no—
129C42—22no—
130C42—22no—
131C42—81no—
132C42C2×D412yes—
133C42#4112yes—
134C23C22×D411yescharacteristic
135Q8—22no—
136Q8—22no—
137Q8—42no—
138Q8—84no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—22no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—22no—
146C2×C4—22no—
147C2×C4—22no—
148C2×C4—22no—
149C2×C4—22no—
150C2×C4—42no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—42no—
156C2×C4—42no—
157C2×C4—42no—
158C2×C4—41no—
159C2×C4—42no—
160C2×C4—41no—
161C2×C4—42no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4#12112yes—
165C2×C4#12112yes—
166C2×C4C22×D411yescharacteristic
167C2×C4C2×#4111yescharacteristic
168C2×C42−1+412yes—
169C2×C42−1+412yes—
170C8—41no—
171C8—42no—
172C8—41no—
173C22C2×#12111yescharacteristic
174C22#53612yes—
175C22#57611yescharacteristic
176C22#57711yescharacteristic
177C22#57812yes—
178C4—22no—
179C4—22no—
180C4—42no—
181C4—42no—
182C4—42no—
183C4—42no—
184C4—82no—
185C4—81no—
186C4—81no—
187C4—82no—
188C4#53611yescharacteristic
189C4#53611yescharacteristic
190C4#54112yes—
191C2#262111yescharacteristic
192C2#304411yescharacteristic
193C2#304511yescharacteristic
194C2#324212yes—
195C2#324312yes—
subgroupG/H
center, socle, prime radicalC23C22×D4
commutator, Frattini, cosocleC22×C4C24
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #376 ◁ 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
C2×#4792
C2×#4772
#26602
#23202
#20852
#20832
#20742
#20722
#19892
#19882
#18322