Finite Group Databasebeta

← #10375

Subgroups — #10375

Order 256.

233 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 233 conjugacy classes of subgroups — too many to draw. Only its 57 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#2549C211yesmaximal, characteristic
2#1996C211yesmaximal, characteristic
3#1520C211yesmaximal, characteristic
4C2×#328C211yesmaximal, characteristic
5#1294C211yesmaximal, characteristic
6#1289C211yesmaximal, characteristic
7#1282C211yesmaximal, characteristic
8C2×C22⋊Q8—21no—
9C2×C22⋊Q8C2211yescharacteristic
10C2×C22⋊C8C2211yescharacteristic
11C2×C22⋊C8C2211yescharacteristic
12#398—21no—
13#395—21no—
14#391—21no—
15#389—21no—
16#385—21no—
17#380C2211yescharacteristic
18#380C2211yescharacteristic
19C4×C22⋊C4C2211yescharacteristic
20C2×#95C2211yescharacteristic
21#342—21no—
22#342—21no—
23#328—21no—
24#328—21no—
25#328—21no—
26#328—21no—
27C22×Q8—21no—
28C22×Q8Q811yescharacteristic, complemented
29C23×C4—21no—
30C23×C4C2311yescharacteristic
31C22×C8—21no—
32C22×C8—21no—
33C22⋊Q8—21no—
34C22⋊Q8—21no—
35C22⋊Q8—21no—
36C22⋊Q8—21no—
37C22⋊Q8—42no—
38C22⋊Q8—42no—
39C2×C4⋊C4—21no—
40C2×C4⋊C4—21no—
41C2×C4⋊C4—21no—
42C2×C4⋊C4—21no—
43C2×C4⋊C4—21no—
44C2×C4⋊C4—21no—
45C2×C4⋊C4—21no—
46C2×C4⋊C4—21no—
47C2×C4⋊C4Q811yescharacteristic, complemented
48C2×C22⋊C4—21no—
49C2×C22⋊C4—21no—
50C2×C22⋊C4—21no—
51C2×C22⋊C4D411yescharacteristic
52C2×C22⋊C4D411yescharacteristic
53C2×C42—21no—
54C22⋊C8—21no—
55C22⋊C8—21no—
56C22⋊C8—21no—
57C22⋊C8—21no—
58#95—21no—
59#95—21no—
60#95—21no—
61#95—21no—
62#95—21no—
63#95D411yescharacteristic
64#95D411yescharacteristic
65#95D411yescharacteristic
66#95D411yescharacteristic
67C24C2×D411yescharacteristic
68C2×Q8—21no—
69C2×Q8—21no—
70C2×Q8—42no—
71C2×Q8—42no—
72C2×Q8—81no—
73C2×Q8—81no—
74C22×C4—21no—
75C22×C4—21no—
76C22×C4—21no—
77C22×C4—21no—
78C22×C4—21no—
79C22×C4—21no—
80C22×C4—21no—
81C22×C4—21no—
82C22×C4—42no—
83C22×C4—41no—
84C22×C4—41no—
85C22×C4—41no—
86C22×C4—81no—
87C22×C4—81no—
88C22×C4C2×D411yescharacteristic
89C22×C4C2×D411yescharacteristic
90C22×C4C2×Q811yescharacteristic
91C22×C4#4111yescharacteristic
92C22×C4#4111yescharacteristic
93C22×C4#4111yescharacteristic
94C2×C8—41no—
95C2×C8—41no—
96C2×C8—81no—
97C2×C8—81no—
98C4⋊C4—21no—
99C4⋊C4—21no—
100C4⋊C4—42no—
101C4⋊C4—42no—
102C4⋊C4—42no—
103C4⋊C4—42no—
104C4⋊C4—41no—
105C4⋊C4—41no—
106C4⋊C4—81no—
107C4⋊C4—81no—
108C4⋊C4—81no—
109C22⋊C4—21no—
110C22⋊C4—21no—
111C22⋊C4—41no—
112C22⋊C4—41no—
113C22⋊C4—41no—
114C22⋊C4—41no—
115C22⋊C4—41no—
116C22⋊C4—41no—
117C22⋊C4SD1612yes—
118C22⋊C4Q1612yes—
119C42—81no—
120C23—41no—
121C23—41no—
122C23#12011yescharacteristic
123C23C22⋊Q811yescharacteristic
124C23#12411yescharacteristic
125C23C2×SD1611yescharacteristic
126C23C2×Q1611yescharacteristic
127C23AGL(1,ℤ/8)11yescharacteristic
128C23#13711yescharacteristic
129Q8—81no—
130Q8—81no—
131Q8—84no—
132C2×C4—22no—
133C2×C4—22no—
134C2×C4—22no—
135C2×C4—41no—
136C2×C4—41no—
137C2×C4—41no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—41no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—82no—
159C2×C4—82no—
160C2×C4—81no—
161C2×C4—81no—
162C2×C4—81no—
163C2×C4—81no—
164C2×C4—81no—
165C2×C4C22⋊Q811yescharacteristic
166C2×C4C22⋊Q811yescharacteristic
167C2×C4#12411yescharacteristic
168C2×C4#12411yescharacteristic
169C8—81no—
170C8—81no—
171C22—21no—
172C22—21no—
173C22—21no—
174C22—21no—
175C22—21no—
176C22—21no—
177C22—41no—
178C22—41no—
179C22—41no—
180C22—41no—
181C22#39311yescharacteristic
182C22#45011yescharacteristic
183C22#45111yescharacteristic
184C22#47511yescharacteristic
185C22#47711yescharacteristic
186C22#48711yescharacteristic
187C22#48911yescharacteristic
188C4—21no—
189C4—21no—
190C4—21no—
191C4—21no—
192C4—42no—
193C4—42no—
194C4—42no—
195C4—81no—
196C4—81no—
197C4—81no—
198C4—81no—
199C4—81no—
200C4—161no—
201C2—21no—
202C2—21no—
203C2—21no—
204C2—21no—
205C2—21no—
206C2—21no—
207C2#202411yescharacteristic
208C2#203111yescharacteristic
209C2#203211yescharacteristic
subgroupG/H
center, socleC22#393
commutator, Frattini, cosocleC23×C4C23
prime radicalC24C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C23×C4 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
28. C22×Q8Q8semidirect
47. C2×C4⋊C4Q8semidirect

Maximal subgroups

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

subgroupindex
#25492
#19962
#15202
C2×#3282
#12942
#12892
#12822