Finite Group Databasebeta

← #9959

Subgroups — #9959

Order 256.

284 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 63 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#3189C211yesmaximal, characteristic
2C2×#484C211yesmaximal, characteristic
3#2502C211yesmaximal, characteristic
4#1996C211yesmaximal, characteristic
5#1824C211yesmaximal, characteristic
6#1520C211yesmaximal, characteristic
7#1282C211yesmaximal, characteristic
8C2×C22⋊Q8C2211yescharacteristic
9C2×C22⋊Q8C2211yescharacteristic
10C22×C4⋊C4C2211yescharacteristic
11#484—22no—
12#484—21no—
13#484—21no—
14#484—22no—
15#467—22no—
16#451—21no—
17#451—21no—
18C2×#107—21no—
19C2×#103—21no—
20C2×C22⋊C8C2211yescharacteristic
21C2×C22⋊C8C2211yescharacteristic
22#398—22no—
23#391—21no—
24#385—22no—
25#384—21no—
26#380C2211yescharacteristic
27C4×C22⋊C4C2211yescharacteristic
28#342—22no—
29#340—22no—
30#328—22no—
31C22×Q8D411yescharacteristic
32C22×Q8D411yescharacteristic
33C23×C4—21no—
34C23×C4C2311yescharacteristic
35C2×Q16—22no—
36C22×C8—21no—
37C22×C8D412yes—
38C22⋊Q8—21no—
39C22⋊Q8—21no—
40C22⋊Q8—21no—
41C22⋊Q8—21no—
42C22⋊Q8—21no—
43C22⋊Q8—21no—
44C22⋊Q8—21no—
45C22⋊Q8—21no—
46C2×C4⋊C4—21no—
47C2×C4⋊C4—21no—
48C2×C4⋊C4—21no—
49C2×C4⋊C4—21no—
50C2×C4⋊C4—21no—
51C2×C4⋊C4—21no—
52C2×C4⋊C4—21no—
53C2×C4⋊C4—21no—
54C2×C4⋊C4—24no—
55C2×C4⋊C4D412yes—
56C2×C4⋊C4D411yescharacteristic
57C2×C4⋊C4D411yescharacteristic
58C2×C22⋊C4—21no—
59C2×C22⋊C4—21no—
60C2×C22⋊C4—21no—
61C2×C22⋊C4D412yes—
62C2×C42—21no—
63#107—24no—
64#107—22no—
65#103—24no—
66#103—22no—
67#103—22no—
68C22⋊C8—21no—
69C22⋊C8—21no—
70C22⋊C8—21no—
71C22⋊C8D412yes—
72#95—24no—
73#95—21no—
74#95—21no—
75C24C2×D411yescharacteristic
76C2×Q8—21no—
77C2×Q8—21no—
78C2×Q8—21no—
79C2×Q8—21no—
80C2×Q8—42no—
81C2×Q8—42no—
82C22×C4—22no—
83C22×C4—21no—
84C22×C4—22no—
85C22×C4—21no—
86C22×C4—21no—
87C22×C4—21no—
88C22×C4—42no—
89C22×C4—41no—
90C22×C4—41no—
91C22×C4—41no—
92C22×C4—82no—
93C22×C4C2×D411yescharacteristic
94C22×C4C2×D411yescharacteristic
95C22×C4C2×D411yescharacteristic
96C22×C4C2×D411yescharacteristic
97C22×C4C2×D411yescharacteristic
98C22×C4#4111yescharacteristic
99Q16—82no—
100C2×C8—22no—
101C2×C8—22no—
102C2×C8—42no—
103C2×C8—42no—
104C4⋊C4—22no—
105C4⋊C4—21no—
106C4⋊C4—21no—
107C4⋊C4—21no—
108C4⋊C4—22no—
109C4⋊C4—21no—
110C4⋊C4—42no—
111C4⋊C4—41no—
112C4⋊C4—41no—
113C4⋊C4—41no—
114C4⋊C4—41no—
115C4⋊C4—41no—
116C4⋊C4—41no—
117C4⋊C4—84no—
118C22⋊C4—22no—
119C22⋊C4—41no—
120C22⋊C4—41no—
121C22⋊C4—41no—
122C22⋊C4—41no—
123C22⋊C4—42no—
124C22⋊C4Q1614yescomplemented
125C42—42no—
126C23—41no—
127C23—41no—
128C23#12011yescharacteristic
129C23#12111yescharacteristic
130C23#12711yescharacteristic
131C23C2×Q1612yes—
132C23#13712yes—
133Q8—42no—
134Q8—42no—
135Q8—42no—
136Q8—81no—
137C2×C4—22no—
138C2×C4—22no—
139C2×C4—22no—
140C2×C4—24no—
141C2×C4—41no—
142C2×C4—41no—
143C2×C4—41no—
144C2×C4—42no—
145C2×C4—42no—
146C2×C4—42no—
147C2×C4—44no—
148C2×C4—42no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—42no—
154C2×C4—82no—
155C2×C4—82no—
156C2×C4—81no—
157C2×C4—81no—
158C2×C4—81no—
159C2×C4—81no—
160C2×C4—81no—
161C2×C4#12011yescharacteristic
162C2×C4#12011yescharacteristic
163C2×C4#12111yescharacteristic
164C2×C4#12111yescharacteristic
165C8—42no—
166C8—42no—
167C22—21no—
168C22—21no—
169C22—21no—
170C22—21no—
171C22—21no—
172C22—21no—
173C22—42no—
174C22—42no—
175C22#39211yescharacteristic
176C22#45112yes—
177C22#46212yes—
178C22#49411yescharacteristic
179C22#49711yescharacteristic
180C4—21no—
181C4—21no—
182C4—21no—
183C4—44no—
184C4—81no—
185C4—82no—
186C4—81no—
187C4—81no—
188C4—81no—
189C4—161no—
190C4#45812yes—
191C2—22no—
192C2—21no—
193C2—22no—
194C2—21no—
195C2#200811yescharacteristic
196C2#201611yescharacteristic
197C2#202211yescharacteristic
subgroupG/H
center, socleC22#392
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
124. C22⋊C4Q16semidirect

Maximal subgroups

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

subgroupindex
#31892
C2×#4842
#25022
#19962
#18242
#15202
#12822