Finite Group Databasebeta

← #32824

Subgroups — #32824

Order 256.

308 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 109 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#2864C211yesmaximal, characteristic
2#2862C211yesmaximal, characteristic
3#2097C212yesmaximal
4#2074C212yesmaximal
5#2068C212yesmaximal
6#2066C212yesmaximal
7#2058C211yesmaximal, characteristic
8#2057C211yesmaximal, characteristic
9#2043C211yesmaximal, characteristic
10#2043C211yesmaximal, characteristic
11#1831C211yesmaximal, characteristic
12C2×C4⋊Q8C2211yescharacteristic
13C2×C4⋊Q8C2211yescharacteristic
14C2×#107C2212yes—
15C2×#106C2212yes—
16C2×C4⋊C8C2212yes—
17C2×#103C2212yes—
18C2×#103C2212yes—
19C2×#103C2212yes—
20C2×#103C2212yes—
21#391—21no—
22#391—21no—
23#391C2212yes—
24#391C2212yes—
25#389C2211yescharacteristic
26#389C2211yescharacteristic
27#389C2211yescharacteristic
28#389C2211yescharacteristic
29#387—21no—
30#387—21no—
31#387—21no—
32#387—21no—
33#382—21no—
34#382—21no—
35#382C2211yescharacteristic
36#382C2211yescharacteristic
37C43C2211yescharacteristic
38#340C2212yes—
39#340C2212yes—
40#336C2211yescharacteristic
41#336C2211yescharacteristic
42#336C2212yes—
43C22×Q8—21no—
44C22×Q8C2312yes—
45C22×C8C2312yes—
46C22×C8C2312yes—
47C4⋊Q8—42no—
48C4⋊Q8—42no—
49C2×C4⋊C4—21no—
50C2×C4⋊C4—21no—
51C2×C4⋊C4—21no—
52C2×C4⋊C4—21no—
53C2×C4⋊C4—21no—
54C2×C4⋊C4—21no—
55C2×C4⋊C4—21no—
56C2×C4⋊C4C2312yes—
57C2×C4⋊C4C2311yescharacteristic
58C2×C4⋊C4C2311yescharacteristic
59C2×C4⋊C4C2311yescharacteristic
60C2×C4⋊C4C2311yescharacteristic
61C2×C42D411yescharacteristic
62C2×C42D411yescharacteristic
63C2×C42D411yescharacteristic
64C2×C42D411yescharacteristic
65C2×C42C2311yescharacteristic
66C2×C42C2311yescharacteristic
67C2×C42C2311yescharacteristic
68#107—42no—
69#106—42no—
70C4⋊C8—42no—
71#103—42no—
72#103—42no—
73#103—42no—
74#103—42no—
75#95—22no—
76#95—22no—
77#95—22no—
78#95—22no—
79#95—21no—
80#95—21no—
81#95—21no—
82#95—21no—
83#95—21no—
84#95—21no—
85#95—21no—
86#95—21no—
87C2×Q8—22no—
88C2×Q8—22no—
89C2×Q8—22no—
90C2×Q8—22no—
91C2×Q8—22no—
92C2×Q8—22no—
93C2×Q8—42no—
94C2×Q8—42no—
95C2×Q8—42no—
96C22×C4—21no—
97C22×C4—21no—
98C22×C4—21no—
99C22×C4—21no—
100C22×C4—22no—
101C22×C4—22no—
102C22×C4C2×D411yescharacteristic
103C22×C4C2×D411yescharacteristic
104C22×C4C2×D411yescharacteristic
105C22×C4C2×D411yescharacteristic
106C22×C4C2×D411yescharacteristic
107C22×C4C2×D411yescharacteristic
108C22×C4C2411yescharacteristic
109C2×C8—22no—
110C2×C8—22no—
111C2×C8—22no—
112C2×C8—22no—
113C2×C8—22no—
114C2×C8—22no—
115C4⋊C4—21no—
116C4⋊C4—21no—
117C4⋊C4—22no—
118C4⋊C4—22no—
119C4⋊C4—22no—
120C4⋊C4—22no—
121C4⋊C4—21no—
122C4⋊C4—21no—
123C4⋊C4—42no—
124C4⋊C4—42no—
125C4⋊C4—42no—
126C4⋊C4—42no—
127C4⋊C4—42no—
128C4⋊C4—42no—
129C4⋊C4—42no—
130C42—22no—
131C42—22no—
132C42—22no—
133C42—21no—
134C42—22no—
135C42—21no—
136C42—22no—
137C42—41no—
138C23C22×D411yescharacteristic
139Q8—42no—
140Q8—42no—
141Q8—42no—
142Q8—42no—
143Q8—84no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—42no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—42no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—42no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—42no—
177C2×C4#13512yes—
178C2×C4#13712yes—
179C2×C4#13712yes—
180C2×C4H(5,𝔽2)11yescharacteristic
181C2×C4H(5,𝔽2)12yes—
182C2×C42−1+412yes—
183C2×C42−1+411yescharacteristic
184C8—42no—
185C8—42no—
186C22#53511yescharacteristic
187C22#53611yescharacteristic
188C22#53711yescharacteristic
189C22C2×#13511yescharacteristic
190C22C2×#13711yescharacteristic
191C22C2×#13711yescharacteristic
192C22#57511yescharacteristic
193C4—22no—
194C4—22no—
195C4—22no—
196C4—41no—
197C4—41no—
198C4—41no—
199C4—82no—
200C4—81no—
201C4—82no—
202C4—81no—
203C4—81no—
204C4—81no—
205C4#56212yes—
206C4#56312yes—
207C2#282011yescharacteristic
208C2#321111yescharacteristic
209C2#321811yescharacteristic
210C2#323111yescharacteristic
211C2#323711yescharacteristic
212C2#324811yescharacteristic
213C2#325211yescharacteristic
subgroupG/H
center, socle, prime radicalC23C22×D4
commutator, Frattini, cosocleC22×C4C24
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C43 ◁ 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
#28642
#28622
#20972
#20742
#20682
#20662
#20582
#20572
#20432
#18312